Chern-Simons Term for BF Theory and Gravity as a Generalized Topological Field Theory in Fo

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PACSnumbers1215Ff,1130Hv,1210Dm,1125Mj…

a r X i v :0803.2889v 2 [h e p -p h ] 14 J u l 2008Mapping Out SU (5)GUTs with Non-Abelian Discrete Flavor SymmetriesFlorian Plentinger ∗and Gerhart Seidl †Institut f¨u r Physik und Astrophysik,Universit¨a t W¨u rzburg,Am Hubland,D 97074W¨u rzburg,Germany(Dated:December 25,2013)We construct a class of supersymmetric SU (5)GUT models that produce nearly tribimaximal lepton mixing,the observed quark mixing matrix,and the quark and lepton masses,from discrete non-Abelian ﬂavor symmetries.The SU (5)GUTs are formulated on ﬁve-dimensional throats in the ﬂat limit and the neutrino masses become small due to the type-I seesaw mechanism.The discrete non-Abelian ﬂavor symmetries are given by semi-direct products of cyclic groups that are broken at the infrared branes at the tip of the throats.As a result,we obtain SU (5)GUTs that provide a combined description of non-Abelian ﬂavor symmetries and quark-lepton complementarity.PACS numbers:12.15.Ff,11.30.Hv,12.10.Dm,One possibility to explore the physics of grand uniﬁed theories (GUTs)[1,2]at low energies is to analyze the neutrino sector.This is due to the explanation of small neutrino masses via the seesaw mechanism [3,4],which is naturally incorporated in GUTs.In fact,from the perspective of quark-lepton uniﬁcation,it is interesting to study in GUTs the drastic diﬀerences between the masses and mixings of quarks and leptons as revealed by current neutrino oscillation data.In recent years,there have been many attempts to re-produce a tribimaximal mixing form [5]for the leptonic Pontecorvo-Maki-Nakagawa-Sakata (PMNS)[6]mixing matrix U PMNS using non-Abelian discrete ﬂavor symme-tries such as the tetrahedral [7]and double (or binary)tetrahedral [8]groupA 4≃Z 3⋉(Z 2×Z 2)and T ′≃Z 2⋉Q,(1)where Q is the quaternion group of order eight,or [9]∆(27)≃Z 3⋉(Z 3×Z 3),(2)which is a subgroup of SU (3)(for reviews see, e.g.,Ref.[10]).Existing models,however,have generally dif-ﬁculties to predict also the observed fermion mass hierar-chies as well as the Cabibbo-Kobayashi-Maskawa (CKM)quark mixing matrix V CKM [11],which applies especially to GUTs (for very recent examples,see Ref.[12]).An-other approach,on the other hand,is oﬀered by the idea of quark-lepton complementarity (QLC),where the so-lar neutrino angle is a combination of maximal mixing and the Cabibbo angle θC [13].Subsequently,this has,in an interpretation of QLC [14,15],led to a machine-aided survey of several thousand lepton ﬂavor models for nearly tribimaximal lepton mixing [16].Here,we investigate the embedding of the models found in Ref.[16]into ﬁve-dimensional (5D)supersym-metric (SUSY)SU (5)GUTs.The hierarchical pattern of quark and lepton masses,V CKM ,and nearly tribi-maximal lepton mixing,arise from the local breaking of non-Abelian discrete ﬂavor symmetries in the extra-dimensional geometry.This has the advantage that theFIG.1:SUSY SU (5)GUT on two 5D intervals or throats.The zero modes of the matter ﬁelds 10i ,5H,24H ,and the gauge supermul-tiplet,propagate freely in the two throats.scalar sector of these models is extremely simple without the need for a vacuum alignment mechanism,while of-fering an intuitive geometrical interpretation of the non-Abelian ﬂavor symmetries.As a consequence,we obtain,for the ﬁrst time,a realization of non-Abelian ﬂavor sym-metries and QLC in SU (5)GUTs.We will describe our models by considering a speciﬁc minimal realization as an example.The main features of this example model,however,should be viewed as generic and representative for a large class of possible realiza-tions.Our model is given by a SUSY SU (5)GUT in 5D ﬂat space,which is deﬁned on two 5D intervals that have been glued together at a common endpoint.The geom-etry and the location of the 5D hypermultiplets in the model is depicted in FIG.1.The two intervals consti-tute a simple example for a two-throat setup in the ﬂat limit (see,e.g.,Refs.[17,18]),where the two 5D inter-vals,or throats,have the lengths πR 1and πR 2,and the coordinates y 1∈[0,πR 1]and y 2∈[0,πR 2].The point at y 1=y 2=0is called ultraviolet (UV)brane,whereas the two endpoints at y 1=πR 1and y 2=πR 2will be referred to as infrared (IR)branes.The throats are supposed to be GUT-scale sized,i.e.1/R 1,2 M GUT ≃1016GeV,and the SU (5)gauge supermultiplet and the Higgs hy-permultiplets 5H and2neously broken to G SM by a 24H bulk Higgs hypermulti-plet propagating in the two throats that acquires a vac-uum expectation value pointing in the hypercharge direc-tion 24H ∝diag(−12,13,15i ,where i =1,2,3is the generation index.Toobtainsmall neutrino masses via the type-I seesaw mechanism [3],we introduce three right-handed SU (5)singlet neutrino superﬁelds 1i .The 5D Lagrangian for the Yukawa couplings of the zero mode fermions then readsL 5D =d 2θ δ(y 1−πR 1) ˜Y uij,R 110i 10j 5H +˜Y d ij,R 110i 5H +˜Y νij,R 15j5i 1j 5H +M R ˜Y R ij,R 21i 1j+h.c. ,(3)where ˜Y x ij,R 1and ˜Y x ij,R 2(x =u,d,ν,R )are Yukawa cou-pling matrices (with mass dimension −1/2)and M R ≃1014GeV is the B −L breaking scale.In the four-dimensional (4D)low energy eﬀective theory,L 5D gives rise to the 4D Yukawa couplingsL 4D =d 2θ Y u ij 10i 10j 5H +Y dij10i 5H +Y νij5i ∼(q i 1,q i 2,...,q i m ),(5)1i ∼(r i 1,r i 2,...,r im ),where the j th entry in each row vector denotes the Z n jcharge of the representation.In the 5D theory,we sup-pose that the group G A is spontaneously broken by singly charged ﬂavon ﬁelds located at the IR branes.The Yukawa coupling matrices of quarks and leptons are then generated by the Froggatt-Nielsen mechanism [21].Applying a straightforward generalization of the ﬂavor group space scan in Ref.[16]to the SU (5)×G A represen-tations in Eq.(5),we ﬁnd a large number of about 4×102ﬂavor models that produce the hierarchies of quark and lepton masses and yield the CKM and PMNS mixing angles in perfect agreement with current data.A distri-bution of these models as a function of the group G A for increasing group order is shown in FIG.2.The selection criteria for the ﬂavor models are as follows:First,all models have to be consistent with the quark and charged3 lepton mass ratiosm u:m c:m t=ǫ6:ǫ4:1,m d:m s:m b=ǫ4:ǫ2:1,(6)m e:mµ:mτ=ǫ4:ǫ2:1,and a normal hierarchical neutrino mass spectrumm1:m2:m3=ǫ2:ǫ:1,(7)whereǫ≃θC≃0.2is of the order of the Cabibbo angle.Second,each model has to reproduce the CKM anglesV us∼ǫ,V cb∼ǫ2,V ub∼ǫ3,(8)as well as nearly tribimaximal lepton mixing at3σCLwith an extremely small reactor angle 1◦.In perform-ing the group space scan,we have restricted ourselves togroups G A with orders roughly up to 102and FIG.2shows only groups admitting more than three valid mod-els.In FIG.2,we can observe the general trend thatwith increasing group order the number of valid modelsper group generally increases too.This rough observa-tion,however,is modiﬁed by a large“periodic”ﬂuctu-ation of the number of models,which possibly singlesout certain groups G A as particularly interesting.Thehighly populated groups would deserve further system-atic investigation,which is,however,beyond the scopeof this paper.From this large set of models,let us choose the groupG A=Z3×Z8×Z9and,in the notation of Eq.(5),thecharge assignment101∼(1,1,6),102∼(0,3,1),103∼(0,0,0),52∼(0,7,0),52↔4FIG.3:Eﬀect of the non-Abelian ﬂavor symmetry on θ23for a 10%variation of all Yukawa couplings.Shown is θ23as a function of ǫfor the ﬂavor group G A (left)and G A ⋉G B (right).The right plot illustrates the exact prediction of the zeroth order term π/4in the expansion θ23=π/4+ǫ/√2and the relation θ13≃ǫ2.The important point is that in the expression for θ23,the leading order term π/4is exactly predicted by thenon-Abelian ﬂavor symmetry G F =G A ⋉G B (see FIG.3),while θ13≃θ2C is extremely small due to a suppression by the square of the Cabibbo angle.We thus predict a devi-ation ∼ǫ/√2,which is the well-known QLC relation for the solar angle.There have been attempts in the literature to reproduce QLC in quark-lepton uniﬁed models [26],however,the model presented here is the ﬁrst realization of QLC in an SU (5)GUT.Although our analysis has been carried out for the CP conserving case,a simple numerical study shows that CP violating phases (cf.Ref.[27])relevant for neutri-noless double beta decay and leptogenesis can be easily included as well.Concerning proton decay,note that since SU (5)is bro-ken by a bulk Higgs ﬁeld,the broken gauge boson masses are ≃M GUT .Therefore,all fermion zero modes can be localized at the IR branes of the throats without intro-ducing rapid proton decay through d =6operators.To achieve doublet-triplet splitting and suppress d =5pro-ton decay,we may then,e.g.,resort to suitable extensions of the Higgs sector [28].Moreover,although the ﬂavor symmetry G F is global,quantum gravity eﬀects might require G F to be gauged [29].Anomalies can then be canceled by Chern-Simons terms in the 5D bulk.We emphasize that the above discussion is focussed on a speciﬁc minimal example realization of the model.Many SU (5)GUTs with non-Abelian ﬂavor symmetries,however,can be constructed along the same lines by varying the ﬂavor charge assignment,choosing diﬀerent groups G F ,or by modifying the throat geometry.A de-tailed analysis of these models and variations thereof will be presented in a future publication [30].To summarize,we have discussed the construction of 5D SUSY SU (5)GUTs that yield nearly tribimaximal lepton mixing,as well as the observed CKM mixing matrix,together with the hierarchy of quark and lepton masses.Small neutrino masses are generated only by the type-I seesaw mechanism.The fermion masses and mixings arise from the local breaking of non-Abelian ﬂavor symmetries at the IR branes of a ﬂat multi-throat geometry.For an example realization,we have shown that the non-Abelian ﬂavor symmetries can exactly predict the leading order term π/4in the sum rule for the atmospheric mixing angle,while strongly suppress-ing the reactor angle.This makes this class of models testable in future neutrino oscillation experiments.In addition,we arrive,for the ﬁrst time,at a combined description of QLC and non-Abelian ﬂavor symmetries in SU (5)GUTs.One main advantage of our setup with throats is that the necessary symmetry breaking can be realized with a very simple Higgs sector and that it can be applied to and generalized for a large class of uniﬁed models.We would like to thank T.Ohl for useful comments.The research of F.P.is supported by Research Train-ing Group 1147“Theoretical Astrophysics and Particle Physics ”of Deutsche Forschungsgemeinschaft.G.S.is supported by the Federal Ministry of Education and Re-search (BMBF)under contract number 05HT6WWA.∗********************************.de †**************************.de[1]H.Georgi and S.L.Glashow,Phys.Rev.Lett.32,438(1974);H.Georgi,in Proceedings of Coral Gables 1975,Theories and Experiments in High Energy Physics ,New York,1975.[2]J.C.Pati and A.Salam,Phys.Rev.D 10,275(1974)[Erratum-ibid.D 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2010年诺贝尔经济学奖得主搜寻匹配理论

2010年诺贝尔经济学奖得主产生，彼得•戴蒙德、莫特森和皮萨里德斯三人分享此项殊荣。

有“麻省神童”之称的戴蒙德获奖早在意料之中，他游走于经济学多个领域，取得卓越成就。

我们知戴蒙德得奖，第一反应以为是因“银行挤兑模型”，2008年世界金融危机爆发了很多投资银行遭遇资金逃离之劫，雷曼兄弟因而倒下，虽然“银行挤兑模型”并不完全以投资银行为“目标”，但却对未来银行存在的危机提供一种深刻的理解。

但这次与他人分享奖项，却因为三人在劳动力市场搜寻理论的贡献，三人所建立的DMP模型（以三人名字头一个字母命名）是分析失业率和工资关系的最重要武器。

市场搜寻理论的基本思想是，劳动者在市场上面临很多工作机会，只有当某个工作机会提供的工资水平大于劳动者的保留工资水平时，劳动者才会接受该工作，从而结束失业状态，在此之前，劳动者会一直处于失业状态。

市场搜寻理论可以解释现实中的一些失业问题，但也存在一个缺陷。

失业应该是劳动力需求和劳动力供给两方面因素共同作用的一个结果，但是，市场搜寻理论只考虑了劳动力供给因素。

它隐含的假设是，只要劳动者想工作他一定能找到工作。

搜寻理论其实是一个庞大的理论群。

在以阿罗-德布鲁模型为集大成者的老式经济学中，劳动力市场是理想的、无摩擦的。

厂商给什么价就会要到什么样的工人，工人愿意出多少力就会得到多少工资。

厂商不在乎失去工人，只要能给出市场价；工人也不在乎失去工作，只要他提高努力水平就能得到新的雇佣。

毫无疑问，这是一个不明智的假设，从这个幼稚假设中得出的结论是工人失业是因为他们懒得工作（不提高努力水平），失业根本就不是一个经济学问题。

经济学家施蒂格勒为搜寻理论拉开序幕，不过他研究的是一般商品的信息搜寻，而不是劳动力市场工作搜寻。

但是，他开创了一种范式。

过去商品市场有一个“拍卖人假设”，这也是瓦尔拉斯体系的核心，遵循的是“价高者得”，虚拟出一个拍卖人喊价，然后看回应，从而最终成交。

施蒂格勒建立一种搜寻关系，即买主费尽力气，克服各种信息成本来找卖家，卖家亦是如此。

Insight Problem Solving A Critical Examination of the Possibility

The Journal of Problem Solving • volume 5, no. 1 (Fall 2012)56Insight Problem Solving: A Critical Examination of the Possibilityof Formal TheoryWilliam H. Batchelder 1 and Gregory E. Alexander 1AbstractThis paper provides a critical examination of the current state and future possibility of formal cognitive theory for insight problem solving and its associated “aha!” experience. Insight problems are contrasted with move problems, which have been formally defined and studied extensively by cognitive psychologists since the pioneering work of Alan Newell and Herbert Simon. To facilitate our discussion, a number of classical brainteasers are presented along with their solutions and some conclusions derived from observing the behavior of many students trying to solve them. Some of these problems are interesting in their own right, and many of them have not been discussed before in the psychologi-cal literature. The main purpose of presenting the brainteasers is to assist in discussing the status of formal cognitive theory for insight problem solving, which is argued to be considerably weaker than that found in other areas of higher cognition such as human memory, decision-making, categorization, and perception. We discuss theoretical barri-ers that have plagued the development of successful formal theory for insight problem solving. A few suggestions are made that might serve to advance the field.Keywords Insight problems, move problems, modularity, problem representation1 Department of Cognitive Sciences, University of California Irvine/10.7771/1932-6246.1143Insight Problem Solving: The Possibility of Formal Theory 57• volume 5, no. 1 (Fall 2012)1. IntroductionThis paper discusses the current state and a possible future of formal cognitive theory for insight problem solving and its associated “aha!” experience. Insight problems are con-trasted with so-called move problems defined and studied extensively by Alan Newell and Herbert Simon (1972). These authors provided a formal, computational theory for such problems called the General Problem Solver (GPS), and this theory was one of the first formal information processing theories to be developed in cognitive psychology. A move problem is posed to solvers in terms of a clearly defined representation consisting of a starting state, a description of the goal state(s), and operators that allow transitions from one problem state to another, as in Newell and Simon (1972) and Mayer (1992). A solu-tion to a move problem involves applying operators successively to generate a sequence of transitions (moves) from the starting state through intermediate problem states and finally to a goal state. Move problems will be discussed more extensively in Section 4.6.In solving move problems, insight may be required for selecting productive moves at various states in the problem space; however, for our purposes we are interested in the sorts of problems that are described often as insight problems. Unlike Newell and Simon’s formal definition of move problems, there has not been a generally agreed upon defini-tion of an insight problem (Ash, Jee, and Wiley, 2012; Chronicle, MacGregor, and Ormerod, 2004; Chu and MacGregor, 2011). It is our view that it is not productive to attempt a pre-cise logical definition of an insight problem, and instead we offer a set of shared defining characteristics in the spirit of Wittgenstein’s (1958) definition of ‘game’ in terms of family resemblances. Problems that we will treat as insight problems share many of the follow-ing defining characteristics: (1) They are posed in such a way as to admit several possible problem representations, each with an associated solution search space. (2) Likely initial representations are inadequate in that they fail to allow the possibility of discovering a problem solution. (3) In order to overcome such a failure, it is necessary to find an alternative productive representation of the problem. (4) Finding a productive problem representation may be facilitated by a period of non-solving activity called incubation, and also it may be potentiated by well-chosen hints. (5) Once obtained, a productive representation leads quite directly and quickly to a solution. (6) The solution involves the use of knowledge that is well known to the solver. (7) Once the solution is obtained, it is accompanied by a so-called “aha!” experience. (8) When a solution is revealed to a non-solver, it is grasped quickly, often with a feeling of surprise at its simplicity, akin to an “aha!” experience.It is our position that very little is known empirically or theoretically about the cogni-tive processes involved in solving insight problems. Furthermore, this lack of knowledge stands in stark contrast with other areas of cognition such as human memory, decision-making, categorization, and perception. These areas of cognition have a large number of replicable empirical facts, and many formal theories and computational models exist that attempt to explain these facts in terms of underlying cognitive processes. The main goal58W. H. Batchelder and G. E. Alexander of this paper is to explain the reasons why it has been so difficult to achieve a scientific understanding of the cognitive processes involved in insight problem solving.There have been many scientific books and papers on insight problem solving, start-ing with the seminal work of the Gestalt psychologists Köhler (1925), Duncker (1945), and Wertheimer (1954), as well as the English social psychologist, Wallas (1926). Since the contributions of the early Gestalt psychologists, there have been many journal articles, a few scientific books, such as those by Sternberg and Davidson (1996) and Chu (2009), and a large number of books on the subject by laypersons. Most recently, two excellent critical reviews of insight problem solving have appeared: Ash, Cushen, and Wiley (2009) and Chu and MacGregor (2011).The approach in this paper is to discuss, at a general level, the nature of several fun-damental barriers to the scientific study of insight problem solving. Rather than criticizing particular experimental studies or specific theories in detail, we try to step back and take a look at the area itself. In this effort, we attempt to identify principled reasons why the area of insight problem solving is so resistant to scientific progress. To assist in this approach we discuss and informally analyze eighteen classical brainteasers in the main sections of the paper. These problems are among many that have been posed to hundreds of upper divisional undergraduate students in a course titled “Human Problem Solving” taught for many years by the senior author. Only the first two of these problems can be regarded strictly as move problems in the sense of Newell and Simon, and most of the rest share many of the characteristics of insight problems as described earlier.The paper is divided into five main sections. After the Introduction, Section 2 describes the nature of the problem solving class. Section 3 poses the eighteen brainteasers that will be discussed in later sections of the paper. The reader is invited to try to solve these problems before checking out the solutions in the Appendix. Section 4 lays out six major barriers to developing a deep scientific theory of insight problem solving that we believe are endemic to the field. We argue that these barriers are not present in other, more theo-retically advanced areas of higher cognition such as human memory, decision-making, categorization, and perception. These barriers include the lack of many experimental paradigms (4.1), the lack of a large, well-classified set of stimulus material (4.2), and the lack of many informative behavioral measures (4.3). In addition, it is argued that insight problem solving is difficult to study because it is non-modular, both in the sense of Fodor (1983) but more importantly in several weaker senses of modularity that admit other areas of higher cognition (4.4), the lack of theoretical generalizations about insight problem solv-ing from experiments with particular insight problems (4.5), and the lack of computational theories of human insight (4.6). Finally, in Section 5, we suggest several avenues that may help overcome some of the barriers described in Section 4. These include suggestions for useful classes of insight problems (5.1), suggestions for experimental work with expert problem solvers (5.2), and some possibilities for a computational theory of insight.The Journal of Problem Solving •Insight Problem Solving: The Possibility of Formal Theory 592. Batchelder’s Human Problem Solving ClassThe senior author, William Batchelder, has taught an Upper Divisional Undergraduate course called ‘Human Problem Solving” for over twenty-five years to classes ranging in size from 75 to 100 students. By way of background, his active research is in other areas of the cognitive sciences; however, he maintains a long-term hobby of studying classical brainteasers. In the area of complex games, he achieved the title of Senior Master from the United States Chess Federation, he was an active duplicate bridge player throughout undergraduate and graduate school, and he also achieved a reasonable level of skill in the game of Go.The content of the problem-solving course is split into two main topics. The first topic involves encouraging students to try their hand at solving a number of famous brainteasers drawn from the sizeable folklore of insight problems, especially the work of Martin Gardner (1978, 1982), Sam Loyd (1914), and Raymond Smullyan (1978). In addition, games like chess, bridge, and Go are discussed. The second topic involves presenting the psychological theory of thinking and problem solving, and in most cases the material is organized around developments in topics that are covered in the first eight chapters of Mayer (1992). These topics include work of the Gestalt psychologists on problem solving, discussion of experiments and theories concerning induction and deduction, present-ing the work on move problems, including the General Problem Solver (Newell & Simon, 1972), showing how response time studies can reveal mental architectures, and describing theories of memory representation and question answering.Despite efforts, the structure of the course does not reflect a close overlap between its two main topics. The principal reason for this is that in our view the level of theoreti-cal and empirical work on insight problem solving is at a substantially lower level than is the work in almost any other area of cognition dealing with higher processes. The main goal of this paper is to explain our reasons for this pessimistic view. To assist in this goal, it is helpful to get some classical brainteasers on the table. While most of these problems have not been used in experimental studies, the senior author has experienced the solu-tion efforts and post solution discussions of over 2,000 students who have grappled with these problems in class.3. Some Classic BrainteasersIn this section we present eighteen classical brainteasers from the folklore of problem solving that will be discussed in the remainder of the paper. These problems have de-lighted brainteaser connoisseurs for years, and most are capable of giving the solver a large dose of the “aha!” experience. There are numerous collections of these problems in books, and many collections of them are accessible through the Internet. We have selected these problems because they, and others like them, pose a real challenge to any effort to • volume 5, no. 1 (Fall 2012)60W. H. Batchelder and G. E. Alexander develop a deep and general formal theory of human or machine insight problem solving. With the exception of Problems 3.1 and 3.2, and arguably 3.6, the problems are different in important respects from so-called move problems of Newell and Simon (1972) described earlier and in Section 4.6.Most of the problems posed in this section share many of the defining characteristics of insight problems described in Section 1. In particular, they do not involve multiple steps, they require at most a very minimal amount of technical knowledge, and most of them can be solved by one or two fairly simple insights, albeit insights that are rarely achieved in real time by problem solvers. What makes these problems interesting is that they are posed in such a way as to induce solvers to represent the problem information in an unproductive way. Then the main barrier to finding a solution to one of these problems is to overcome a poor initial problem representation. This may involve such things as a re-representation of the problem, the dropping of an implicit constraint on the solution space, or seeing a parallel to some other similar problem. If the solver finds a productive way of viewing the problem, the solution generally follows rapidly and comes with burst of insight, namely the “aha!” experience. In addition, when non-solvers are given the solu-tion they too may experience a burst of insight.What follows next are statements of the eighteen brainteasers. The solutions are presented in the Appendix, and we recommend that after whatever problem solving activity a reader wishes to engage in, that the Appendix is studied before reading the remaining two sections of the paper. As we discuss each problem in the paper, we provide authorship information where authorship is known. In addition, we rephrased some of the problems from their original sources.Problem 3.1. Imagine you have an 8-inch by 8-inch array of 1-inch by 1-inch little squares. You also have a large box of 2-inch by 1-inch rectangular shaped dominoes. Of course it is easy to tile the 64 little squares with dominoes in the sense that every square is covered exactly once by a domino and no domino is hanging off the array. Now sup-pose the upper right and lower left corner squares are cut off the array. Is it possible to tile the new configuration of 62 little squares with dominoes allowing no overlaps and no overhangs?Problem 3.2. A 3-inch by 3-inch by 3-inch cheese cube is made of 27 little 1-inch cheese cubes of different flavors so that it is configured like a Rubik’s cube. A cheese-eating worm devours one of the top corner cubes. After eating any little cube, the worm can go on to eat any adjacent little cube (one that shares a wall). The middlemost little cube is by far the tastiest, so our worm wants to eat through all the little cubes finishing last with the middlemost cube. Is it possible for the worm to accomplish this goal? Could he start with eating any other little cube and finish last with the middlemost cube as the 27th?The Journal of Problem Solving •Insight Problem Solving: The Possibility of Formal Theory 61 Figure 1. The cheese eating worm problem.Problem 3.3. You have ten volumes of an encyclopedia numbered 1, . . . ,10 and shelved in a bookcase in sequence in the ordinary way. Each volume has 100 pages, and to simplify suppose the front cover of each volume is page 1 and numbering is consecutive through page 100, which is the back cover. You go to sleep and in the middle of the night a bookworm crawls onto the bookcase. It eats through the first page of the first volume and eats continuously onwards, stopping after eating the last page of the tenth volume. How many pieces of paper did the bookworm eat through?Figure 2.Bookcase setup for the Bookworm Problem.Problem 3.4. Suppose the earth is a perfect sphere, and an angel fits a tight gold belt around the equator so there is no room to slip anything under the belt. The angel has second thoughts and adds an inch to the belt, and fits it evenly around the equator. Could you slip a dime under the belt?• volume 5, no. 1 (Fall 2012)62W. H. Batchelder and G. E. Alexander Problem 3.5. Consider the cube in Figure 1 and suppose the top and bottom surfaces are painted red and the other four sides are painted blue. How many little cubes have at least one red and at least one blue side?Problem 3.6. Look at the nine dots in Figure 3. Your job is to take a pencil and con-nect them using only three straight lines. Retracing a line is not allowed and removing your pencil from the paper as you draw is not allowed. Note the usual nine-dot problem requires you to do it with four lines; you may want to try that stipulation as well. Figure 3.The setup for the Nine-Dot Problem.Problem 3.7. You are standing outside a light-tight, well-insulated closet with one door, which is closed. The closet contains three light sockets each containing a working light bulb. Outside the closet, there are three on/off light switches, each of which controls a different one of the sockets in the closet. All switches are off. Your task is to identify which switch operates which light bulb. You can turn the switches off and on and leave them in any position, but once you open the closet door you cannot change the setting of any switch. Your task is to figure out which switch controls which light bulb while you are only allowed to open the door once.Figure 4.The setup of the Light Bulb Problem.The Journal of Problem Solving •Insight Problem Solving: The Possibility of Formal Theory 63• volume 5, no . 1 (Fall 2012)Problem 3.8. We know that any finite string of symbols can be extended in infinitely many ways depending on the inductive (recursive) rule; however, many of these ways are not ‘reasonable’ from a human perspective. With this in mind, find a reasonable rule to continue the following series:Problem 3.9. You have two quart-size beakers labeled A and B. Beaker A has a pint of coffee in it and beaker B has a pint of cream in it. First you take a tablespoon of coffee from A and pour it in B. After mixing the contents of B thoroughly you take a tablespoon of the mixture in B and pour it back into A, again mixing thoroughly. After the two transfers, which beaker, if either, has a less diluted (more pure) content of its original substance - coffee in A or cream in B? (Forget any issues of chemistry such as miscibility).Figure 5. The setup of the Coffee and Cream Problem.Problem 3.10. There are two large jars, A and B. Jar A is filled with a large number of blue beads, and Jar B is filled with the same number of red beads. Five beads from Jar A are scooped out and transferred to Jar B. Someone then puts a hand in Jar B and randomly grabs five beads from it and places them in Jar A. Under what conditions after the second transfer would there be the same number of red beads in Jar A as there are blue beads in Jar B.Problem 3.11. Two trains A and B leave their train stations at exactly the same time, and, unaware of each other, head toward each other on a straight 100-mile track between the two stations. Each is going exactly 50 mph, and they are destined to crash. At the time the trains leave their stations, a SUPERFLY takes off from the engine of train A and flies directly toward train B at 100 mph. When he reaches train B, he turns around instantly, A BCD EF G HI JKLM.............64W. H. Batchelder and G. E. Alexander continuing at 100 mph toward train A. The SUPERFLY continues in this way until the trains crash head-on, and on the very last moment he slips out to live another day. How many miles does the SUPERFLY travel on his zigzag route by the time the trains collide?Problem 3.12. George lives at the foot of a mountain, and there is a single narrow trail from his house to a campsite on the top of the mountain. At exactly 6 a.m. on Satur-day he starts up the trail, and without stopping or backtracking arrives at the top before6 p.m. He pitches his tent, stays the night, and the next morning, on Sunday, at exactly 6a.m., he starts down the trail, hiking continuously without backtracking, and reaches his house before 6 p.m. Must there be a time of day on Sunday where he was exactly at the same place on the trail as he was at that time on Saturday? Could there be more than one such place?Problem 3.13. You are driving up and down a mountain that is 20 miles up and 20 miles down. You average 30 mph going up; how fast would you have to go coming down the mountain to average 60 mph for the entire trip?Problem 3.14. During a recent census, a man told the census taker that he had three children. The census taker said that he needed to know their ages, and the man replied that the product of their ages was 36. The census taker, slightly miffed, said he needed to know each of their ages. The man said, “Well the sum of their ages is the same as my house number.” The census taker looked at the house number and complained, “I still can’t tell their ages.” The man said, “Oh, that’s right, the oldest one taught the younger ones to play chess.” The census taker promptly wrote down the ages of the three children. How did he know, and what were the ages?Problem 3.15. A closet has two red hats and three white hats. Three participants and a Gamesmaster know that these are the only hats in play. Man A has two good eyes, man B only one good eye, and man C is blind. The three men sit on chairs facing each other, and the Gamesmaster places a hat on each man’s head, in such a way that no man can see the color of his own hat. The Gamesmaster offers a deal, namely if any man correctly states the color of his hat, he will get $50,000; however, if he is in error, then he has to serve the rest of his life as an indentured servant to the Gamesmaster. Man A looks around and says, “I am not going to guess.” Then Man B looks around and says, “I am not going to guess.” Finally Man C says, “ From what my friends with eyes have said, I can clearly see that my hat is _____”. He wins the $50,000, and your task is to fill in the blank and explain how the blind man knew the color of his hat.Problem 3.16. A king dies and leaves an estate, including 17 horses, to his three daughters. According to his will, everything is to be divided among his daughters as fol-lows: 1/2 to the oldest daughter, 1/3 to the middle daughter, and 1/9 to the youngest daughter. The three heirs are puzzled as to how to divide the horses among themselves, when a probate lawyer rides up on his horse and offers to assist. He adds his horse to the kings’ horses, so there will be 18 horses. Then he proceeds to divide the horses amongThe Journal of Problem Solving •Insight Problem Solving: The Possibility of Formal Theory 65 the daughters. The oldest gets ½ of the horses, which is 9; the middle daughter gets 6 horses which is 1/3rd of the horses, and the youngest gets 2 horses, 1/9th of the lot. That’s 17 horses, so the lawyer gets on his own horse and rides off with a nice commission. How was it possible for the lawyer to solve the heirs’ problem and still retain his own horse?Problem 3.17. A logical wizard offers you the opportunity to make one statement: if it is false, he will give you exactly ten dollars, and if it is true, he will give you an amount of money other than ten dollars. Give an example of a statement that would be sure to make you rich.Problem 3.18. Discover an interesting sense of the claim that it is in principle impos-sible to draw a perfect map of England while standing in a London flat; however, it is not in principle impossible to do so while living in a New York City Pad.4. Barriers to a Theory of Insight Problem SolvingAs mentioned earlier, our view is that there are a number of theoretical barriers that make it difficult to develop a satisfactory formal theory of the cognitive processes in play when humans solve classical brainteasers of the sort posed in Section 3. Further these barriers seem almost unique to insight problem solving in comparison with the more fully developed higher process areas of the cognitive sciences such as human memory, decision-making, categorization, and perception. Indeed it seems uncontroversial to us that neither human nor machine insight problem solving is well understood, and com-pared to other higher process areas in psychology, it is the least developed area both empirically and theoretically.There are two recent comprehensive critical reviews concerning insight problem solving by Ash, Cushen, and Wiley (2009) and Chu and MacGregor (2011). These articles describe the current state of empirical and theoretical work on insight problem solving, with a focus on experimental studies and theories of problem restructuring. In our view, both reviews are consistent with our belief that there has been very little sustainable progress in achieving a general scientific understanding of insight. Particularly striking is that are no established general, formal theories or models of insight problem solving. By a general formal model of insight problem solving we mean a set of clearly formulated assumptions that lead formally or logically to precise behavioral predictions over a wide range of insight problems. Such a formal model could be posed in terms of a number of formal languages including information processing assumptions, neural networks, computer simulation, stochastic assumptions, or Bayesian assumptions.Since the groundbreaking work by the Gestalt psychologists on insight problem solving, there have been theoretical ideas that have been helpful in explaining the cog-nitive processes at play in solving certain selected insight problems. Among the earlier ideas are Luchins’ concept of einstellung (blind spot) and Duncker’s functional fixedness, • volume 5, no. 1 (Fall 2012)as in Maher (1992). More recently, there have been two developed theoretical ideas: (1) Criterion for Satisfactory Progress theory (Chu, Dewald, & Chronicle, 2007; MacGregor, Ormerod, & Chronicle, 2001), and (2) Representational Change Theory (Knoblich, Ohls-son, Haider, & Rhenius, 1999). We will discuss these theories in more detail in Section 4. While it is arguable that these theoretical ideas have done good work in understanding in detail a few selected insight problems, we argue that it is not at all clear how these ideas can be generalized to constitute a formal theory of insight problem solving at anywhere near the level of generality that has been achieved by formal theories in other areas of higher process cognition.The dearth of formal theories of insight problem solving is in stark contrast with other areas of problem solving discussed in Section 4.6, for example move problems discussed earlier and the more recent work on combinatorial optimization problems such as the two dimensional traveling salesman problem (MacGregor and Chu, 2011). In addition, most other higher process areas of cognition are replete with a variety of formal theories and models. For example, in the area of human memory there are currently a very large number of formal, information processing models, many of which have evolved from earlier mathematical models, as in Norman (1970). In the area of categorization, there are currently several major formal theories along with many variations that stem from earlier theories discussed in Ashby (1992) and Estes (1996). In areas ranging from psycholinguistics to perception, there are a number of formal models based on brain-style computation stemming from Rumelhart, McClelland, and PDP Research Group’s (1987) classic two-volume book on parallel distributed processing. Since Daniel Kahneman’s 2002 Nobel Memorial Prize in the Economic Sciences for work jointly with Amos Tversky developing prospect theory, as in Kahneman and Tversky (1979), psychologically based formal models of human decision-making is a major theoretical area in cognitive psychology today. In our view, there is nothing in the area of insight problem solving that approaches the depth and breadth of formal models seen in the areas mentioned above.In the following subsections, we will discuss some of the barriers that have prevented the development of a satisfactory theory of insight problem solving. Some of the bar-riers will be illustrated with references to the problems in Section 3. Then, in Section 5 we will assuage our pessimism a bit by suggesting how some of these barriers might be removed in future work to facilitate the development of an adequate theory of insight problem solving.4.1 Lack of Many Experimental ParadigmsThere are not many distinct experimental paradigms to study insight problem solving. The standard paradigm is to pick a particular problem, such as one of the ones in Section 3, and present it to several groups of subjects, perhaps in different ways. For example, groups may differ in the way a hint is presented, a diagram is provided, or an instruction。

The Chern-Simons Coefficient in Supersymmetric Non-abelian Chern-Simons Higgs Theories

1 4π
for the systems to be invariant

under large gauge transformation; otherwise the theories are not quantum-mechanically consistent. Therefore, it is interesting to conﬁrm that the quantization condition is not 2
The Chern-Simons Coeﬃcient in Supersymmetric Non-Abelian Chern-Simons Higgs Theories
Hsien-chung Kao†
Department of Physics, Tamkang University, Tamsui, Taiwan 25137, R.O.C.
arXiv:hep-th/9904043v2 14 May 1999
Abstract
By taking into account the eﬀect of the would be Chern-Simons term, we calculate the quantum correction to the Chern-Simons coeﬃcient in supersymmetric Chern-Simons Higgs theories with matter ﬁelds in the fundamental representation of SU (n). Because of supersymmetry, the corrections in the symmetric and Higgs phases are identical. In particular, the correction is vanishing for N = 3 supersymmetric Chern-Simons Higgs theories. The result should be quite general, and have important implication for the more interesting case when the Higgs is in the adjoint representation. PACS number(s):11.10.Kk, 11.10.Gh, 11.15.Ex, 11.30.Pb

理论物理电子书

理论物理电子书理论物理-电子书0000理论物理基础彭桓武Simons B. Concepts in theoretical physics (Cambridge lecture notes, 2002)(T)(273s)Principles of Modern Physics-N E I L A S H B Y-S T A N L E Y C . M I L L E R-University of ColoradoFUNDAMENTALS OF physics-J. Richard Christman0-mathematical physics李代数李超代数及在物理学中的应用孙洪洲群论.及其在粒子物理学中的应用,.高崇寿.1992群论及其在固体物理中的应用【徐婉棠,喀兴林】群论及其在物理中的应用(马中骐)群论习题精解+(马中骐)群论与量子力学物理系群论讲义物理学中的群论(上册).陶瑞宝物理学中的群论基础 A W 约什Geometry_Topology_and Physics-NakaharaGeometry+and+Physics+(Jürgen Jost)Lee J.M. Differential and physical geometry (draft)(721s)数学物理中的微分几何与拓扑学_汪容.浙大版.1998Differential Geometry, Analysis and Physics 。

Jeffrey M. Lee微分几何学及其在物理学中的应用物理学家用微分几何-侯伯宇-侯伯元物理中的张量孙志铭Arnold vol1，2A Guided Tour Of Mathematical Physics (By Roel Snieder, Department Of Geophysics, Utrecht UniversAbramovitz M., Stegun I.A. (eds.) Handbook of mathematical functions (10ed., NBS, 1972)(T)(1037s)Academic Press, Methods of Modern Mathematical Physics -- Vol. 1, Functional AnCourant, Hilbert - Methods of Mathematical Physics Vol. 1 ENG (578p)Introduction+to+Applied+Mathematics-GilbertStrangIntroduction+to+Mathematical+Physics+(Laurie+Cosse y)Math_method_for_Phy_Ken Riley, Michael Hobson and Stephen Bence Cambridge, 1997Szekeres, Peter - A Course in Modern Mathematical Physics - Groups, Hilbert Spaces and Differenti数学物理方法梁昆淼数学物理方法（R.+柯朗、D.+希尔伯特）数学物理方法吴崇试数学物理学中的微分形式数学物理中的几何方法(B·F·舒茨)特殊函数概论王竹溪物理学中的非线性方程刘式适物理学中的数学方法（李政道）1-Classical Mechanics and Fluid MechanicsClassical Mechanics - Goldstein古典力学(戈德斯坦)Hand, Finch Analytical Mechanics (Cup, 1998)(T)(590S)Structure and Interpretation of Classical Mechanics-Gerald Jay Sussman and Jack Wisdom with Meinhard E. Mayer -MIT Press经典力学张启仁2-Statistical And Thermal Physics理论物理学基础教程丛书统计物理学(苏汝铿)量子统计力学 by 张先蔚量子统计物理学(北京大学物理系)统计物理现代教程（上、下册）(雷克)统计物理中的蒙特卡罗模拟方法（含有热力学，难度适中）Reif. Fundamentals of Statistical And Thermal PhysicsBratteli O , Robinson D W Vol 1 Operator Algebras And Quantum Statistical Mechanics (2Ed , SpringHuang K. Statistical mechanics (2ed., Wiley, 1987)(T)(506s)Reichl L.E. A modern course in statistical physics (2ed, Wiley, 1998)(T)(840s)3-Electrodynamics赵凯华-电磁学上宇宙电动力学_阿尔芬引力论和宇宙论：广义相对论的原理和应用-温伯格相对论物理宇宙学讲义俞允强天体物理学【李宗伟、肖兴华】+时空的大尺度结构（原版）- 霍金简明天文学手册-刘步林广义相对论引论广义相对论dirac广义相对论（刘辽）大众天文学【法】弗拉马利翁Jackson J.D. Classical electrodynamics (3ed., Wiley,1999)(ISBN 047130932X)(600dpi)(K)(T)(833s).d（研究生程度的必读教材）JACKSON经典电动力学（上册）（经典之作）J.A.Wheeler E.F.Taylor Spacetime_PhysicsHerbert Neff - Introductory ElectromagneticsElectromagnetics (Rothwell & Cloud, 2001 CRC Press)Electricity+and+Magnetism-MITcourseCohen-Tannoudji Introduction to quantum electrodynamicsBuch_John Wiley. Sons_An Introduction to Modern Cosmology4-Optics（光学经典，全面、很厚，很难）光学原理上册、下册(m.玻恩 e.沃耳夫)Bass M , Et Al (Eds) Osa Handbook Of Optics, Vol 1 (Mgh, 1995)(1606s)Goodman - Geometrical Optics--p1628 - cambridgeWiley,.Modern.Nonlinear.Optics.Part.I.Advances.in. Chemical.Physics.Volume.119.(2001),.2Ed5-Quantum MechanicsClassical and Quantum ChaosCohen-Tannoudji Quantum Mechanics, Vol 1Galindo A., Pascual P. Quantum mechanics I (Springer,1990)(ISBN 0387514066)(T) (431s)量子系统中的几何相位-A.Bohm等Jack_Simons_-_Quantum MechanicsJohn_Norbury_-_Quantum_Mechanics_for_Undergraduate sMathematics+of+Quantum+Computation-Goong.ChenModern Quantum Mechanics And Solutions For The Exercices (J J Sakurai)Nuclear And Particle Physics-NielsWaletPhillips.-.Introduction.to.quantum.mechanics.(2003 )(T)(284s)Quantum Mechanics - Concepts and Applications-Tarun.BiswasShankar-Principles Of Quantum Mechanics 2nd EditionThe Basic Tools Of Quantum MechanicsThe+Physics+of+Phase+Transitions-P. Papon J. Leblond P.H.E. MeijerLecture Notes in Physics-Time+in+Quantum++Mechanics+1J.G. Muga.R. Sala Mayato?I.L. Egusquiza (Eds.)Zaarur E. Schaum's Outline of Quantum Mechanics.. Including Hundreds of Solved Problems (Schaum,1喀兴林-高等量子力学席夫量子力学-繁体中文版量子力学(Messiah)Vol1量子力学（卷I）.曾谨言量子力学“天龙八部”-张永德量子力学+(苏汝铿)量子力学Fermi量子力学讲义（张永德）量子力学原理(狄拉克)量子论的物理原理量子论与原子结构-吴大遒量子物理学导论(MIT)物理学引论Vol4-A.P.French By Tsungp Lee量子物理-赵凯华高等量子力学-张永德6-Field theory量子场论-温伯格1,2,3An Introduction to Quantum FieldTheory(Peskin,Schroeder)(full and revised)Banks,Modern+Quantum+Field+Theory--A+Concise+Intro ductionField.theory,.Roman.S..(2ed.,.Springer,.2005)Giachetta,Advanced+Classical+Field+Theory经典场论Kleinert H. Quantum field theory and particle physicsItep-PARTICLE-PHYSICS-and-field-theory场论I-M.A.ShifmanQuantum Field Theory R ClarksonQuantum+Field+Theory+(M.Srednicki) Quantum+Field+Theory-David McMahon Sundaresan. Handbook of particle physics (CRC, 2001)(T)(439 Tong-Quantum Field Theory Zinn-Justin. Quantum field theory and critical phenomena (1ed., 1989)(K)(150dpi)(T)(924s) 北大2005量子场论讲义（赵光达）量子场论-清华王青讲义规范场论（胡瑶光）粒子和场【卢里着,董明德等译】量子场论(上)【依捷克森,祖柏尔着,杜东生等译】量子场论A.Zee量子场论F.Mandl-G.Shaw量子场论LEWIS-H.RYDER实时统计场论-徐宏华统计物理学中的量子场论方法-Abrikosov微分几何-统一场论超弦理论导论Elias-Kiritsis张秋光《场论》上册朱洪元+量子场论On Wittens 3-manifold Invariants-Kevin WalkerLectures on Topological Quantum Field Theory-J. M. F. Labastidaa-Carlos LozanobGEOMETRY OF 2D TOPOLOGICAL FIELD THEORIES-Boris DUBROVIN-SISSA, TriesteDunne(1999)-Aspects of Chern-Simons Theorylabastida(1998)-Chern-Simons Gauge Theory-- Ten Years After7-Solid state physics（非常好的书）固体物理学（黄昆）固体物理导论C.KittelMechanics Of Solids-Bela I. Sandor-University of Wisconsin-MadisonKleinert H. Gauge fields in condensed matter physics part1(T)(252s)Ashcroft, Neil W, Mermin, David N - Solid State PhysicsAltland & Simons - Concepts Of Theoretical Solid State Physics。

2010诺贝尔物理学奖

2010诺贝尔物理学奖得主:把科研当成快乐的游戏 2010年10月15日 11:16 中国新闻周刊安德烈·海姆和康斯坦丁·诺沃肖洛夫今年的诺贝尔物理学奖可能最具娱乐性：一对师徒用透明胶带在制作铅笔芯的石墨中发现了一种二维平面材料，他们中的一位还曾获得过“搞笑诺贝尔奖”本刊记者/钱炜10月5日，瑞典皇家科学院宣布，将2010年诺贝尔物理学奖授予英国曼彻斯特大学的两位科学家——现年52岁的安德烈·海姆和36岁的康斯坦丁·诺沃肖洛夫，以表彰他们在石墨烯材料方面的卓越研究。

研究：“search”而非“research”石墨烯是怎么被发现的？对此，海姆2008年在接受《科学观察》采访时解释说，除了拥有设备和相关方面的知识，一个重要原因是自己有一种“科研恶习”。

他说，“那段时间里，我关注研究碳纳米管的那拨人，对他们时不时地声称获得这样或那样牛的成果觉得恶心。

我想，我可以做一点不同于碳纳米管的东西，为什么不把碳纳米管剖开呢？于是，就有了后来的研究。

”起初，海姆请实验室新来的一名中国博士生将一块高定向裂解石墨制成薄膜，要求尽可能薄，并给了他一台精巧的抛光机。

三周后，这名博士生拿着培养皿来见海姆，说他成功了。

海姆用显微镜一看，那些石墨碎片估计仍有1000层左右。

海姆希望他能将石墨碎片研磨得更薄一些，但这名博士生最后说：“如果你这么聪明，就自己试试。

”于是这成了一个转折点，海姆决定自己来试试，他就用透明胶带来做这件事。

如今，海姆所用的方法，被业界戏称为“透明胶带技术”。

由于层间的作用力非常弱，石墨很容易剥落脱离。

将石墨放在透明胶带上，反复撕拉 10～20下左右，就获得了10层左右的石墨——这正是海姆当初的实验，他们并没有直接获得石墨烯，但10层左右的石墨就已表现出了足够特殊的物理性能。

海姆曾用磁性克服重力，让一只青蛙漂浮在半空中，因此获得了2000年的“搞笑诺贝尔奖”。

诺贝尔基金会也形容这对师徒“把科学研究当成快乐的游戏”。

Chern-Simons Theory on the Torus

a r X i v :h e p -t h /9210087v 1 16 O c t 1992CHERN-SIMONS THEORY ON THE TORUS 1F.Falceto 2,K.Gaw¸e dzkiIHES,Bures-sur-Yvette,91440,FranceRecently a considerable eﬀort has been invested in understanding Chern-Simons theories from the canonical or covariant points of view.The covariant quantization was used to obtain topological invariants of three dimensional manifolds [1]whereas the canonical point of view [1-5]allowed to relate the states of three dimensional Chern-Simons theory to conformal blocks of two dimensional Wess-Zumino-Witten models.Here we shall discuss the second approach.More precisely we shall study the space of quantum states of the Chern-Simons theory for the group SU (2)on T 2×R and in the presence of Wilson lines {z n }×R ,n =1,···,N,corresponding to representations ρj n of spin j n (acting in spaces V j n ).The gauge freedom is partially ﬁxed by setting the temporal (R -direction)component of the connection to zero.The remaining gauge invariance is imposed on the states (very much like the Gauss law in QED)in terms of a quantum ﬂatness condition.The presence of the Wilson lines contributes source terms to the ﬂattness condition.In the holomorphic quantization `a la Bargmann we pick up a complex structure on the torus T 2by ﬁxing the modular parameter τ=τ1+iτ2∈H .This induces a complex structure in the space of two dimensional (smooth)connections.Integration of the ﬂattness condition leads then to the following picture of the quantum states (see [2],[4],[6],):they are holomorphic functionalsΨ:A01≡Ω01(T 2)⊗sl(2,C )→nV j nsatisfyingΨ(h A 01)=ekS WZW (h −1,A 01)nh (z n )(n )Ψ(A 01),(1)where S WZW is the Wess-Zumino-Witten action coupled to the (0,1)part of the connection whose gauge transformed version h A 01is given byh A01=hA 01h −1+h ¯∂h−1(2)with h in the gauge group G C ≡C ∞(T 2,SL(2,C )).h (z )(n )≡I ⊗···⊗ρj n (h (z ))⊗···⊗I .From (1)it follows that Ψis determined from its value at a point of each gauge orbit.However the space A 01/G C is not a manifold and to study the smoothness of Ψsubject to (1)we need a detailed knowledge of positions and sizes (codimensions)of the G C orbits.First we shall identify A 01with the space of structures of holomorphic SL (2,C )bundles on the trivial bundle T 2×C 2:holomorphic sections of the bundle corresponding to A 01aregiven by maps g with (¯∂+A 01)g =0.This space has been studied in [7]and from there we infer that in our case almost every bundle,except for some submanifolds of complex codimension at least 2,is semistable and all these strata are formed by the union of gauge orbits.From the properties of the stratiﬁcation and the Hartogs theorem,it follows thatevery holomorphic functional on the space of semistable bundles can be uniquely extended to the whole space.Every semistable connection can be gauge transformed into one of the following[8][6]A01u=−uσ3d¯z/(2τ2)u∈CA01α=hα(−σ+d¯z/(2τ2))α=0,12,τ+12uσ+).ThenhαMu d¯z≡hαg u A01u−−→u→0 A01α.From now on we will use a realization of spaces V jn in terms of polynomials of degree at most2j n on which elements of SL(2,C)act by fractional ing this realization we have(from(1))n(e M u(¯z n−z n)h−1α(z n))(n)Ψ(hαM u d¯z)((v n))=eπk(u+α)2/τ2( n e−(α−¯α)z n j n/τ2)(2u)−Jγ(u+α) (e(α−¯α)z n/τ2+2e(α−¯α)z n/τ2uv n) .(5) Now the left hand side is holomorphic in u whereas the right hand side,because of the presence of the u−J factor,is not holomorphic unless∂l0u∂l1v1···∂l N vNγ(u)(vfor every N+1-tuple of non negative integers L≡(l i)such that|L|≡Ni=0l i<J.Conversely,one may see that if(6)holds forα=0,1/2,τ/2,(τ+1)/2thenΨcan beextended to the four codimension1strata A01(α,0).Properties of the stratiﬁcation allow nowto apply inductively Hartogs theorem and to extendΨ,as a holomorphic functional,to all other higher codimension strata.In this way we obtain a quantum state of the theory. Theorem:There is a one to one correspondence between the space of states of Chern-Simons theory in the presence of Wilson lines and the space W fr N(τ,zFrom(4,a-d),the zero-points states are simply the even theta-functions of degree2k, since for J=0condition(6)plays no role.The dimension of the space of even theta-functions is k+1.It is spanned by Kac-Moody charactersχk,j(τ,e2πiu)withﬁxedτand j=0,1/2,...,k/2.States with one insertion.2,τ2.(7,b)To study the dimension d j of the space of solutions of(7,a-b)we shallﬁrst focus on the case of even spin,j∈2N.In that case(7,a)requires even theta-functions for which:e−4πiku α−¯ατ−¯τϑ(−u+α)α=0,12,τ+1The case of odd spin j can be treated in a similar way.Now we have k−1independent odd theta-functions and(7,b)gives2j−2independent conditions.Finally we obtain the same expression(10)for the dimension.It can be shown(see[6])that spaces W fr N(τ,z。

A History of Division 32 (Humanistic Psychology) of the American Psychological Association

Aanstoos, C. Serlin, I., & Greening, T. (2000). History of Division 32 (Humanistic Psychology) of the American Psychological Association. InD. Dewsbury (Ed.), Unification through Division: Histories of thedivisions of the American Psychological Association, Vol. V. Washington, DC: American Psychological Association.A History of Division 32 (Humanistic Psychology) of the AmericanPsychological AssociationChristopher M. Aanstoos, Ilene Serlin, Thomas Greening*Authors' note: The authors thank Carmi Harari, Myron Arons, Gloria Gottsegen, Mark Stern, Amedeo Giorgi, Stanley Krippner and Alvin Mahrer, all early leaders in Division 32s history. Their generous willingness to give their time to be interviewed greatly assisted in the research that led to the chapter. Harari's own written correspondence and other archival materials, which he kindly shared, were also indispensable. Further thanks are owed to Eleanor Criswell, David Elkins, Kirk Schneider, and Myron Arons, without whose supportive efforts the chapter could not have been completed. We also thank Donald Dewsbury, without whose patience and perseverance this chapter would not have reached a final publishable form.A History of Division 32 (Humanistic Psychology) of the AmericanPsychological AssociationChristopher M. Aanstoos, Ilene Serlin, Tom GreeningAs with most complex human endeavors, the history of APA Division 32, Humanistic Psychology, has many facets and lends itself to many narratives and interpretations. Presented here is one version, resulting from the input of three authors and many other people. Readers may wish to read between the lines or project onto the text their own versions. In humanistic psychology, in writing the Division's history, and indeed in psychology itself, there are always texts and subtexts, and multiple "stories" and interpretations. Right and left brains play their parts in the making of history, and in the recording and interpretation of it. This chapter is one history of the Division. Other fascinating chapters could be written about the people involved, the intellectual and interpersonal currents, and the creative, socially responsible, and sometimes spontaneous and chaotic events that underlay this history.Prior History: An Emergent Cultural ZeitgeistHumanistic psychology is sometimes known as the Third Force in contrast to two major orientations in American psychology, behaviorism and psychoanalysis, which, along with the biomedical model, are considered by humanistic psychologists to be reductionistic, mechanistic, and dehumanizing in regard to human beings as whole persons. As one critic of behaviorism put it, "American psychology first lost its soul, then its mind, and finally its consciousness, but it still behaved" (Waters, 1958, p. 278). Inregard to psychoanalysis, Freud's own words present the challenge to which humanistic psychology responded:The moment a man questions the meaning and value oflife he is sick, since objectively neither has any existence;by asking this question one is merely admitting to a storeof unsatisfied libido to which something else must havehappened, a kind of fermentation leading to sadness anddepression. (Freud, 1960, p. 436)Many psychologists were crucial in preparing the ground for what emerged as humanistic psychology's alternative, but three stand out: Abraham Maslow, Carl Rogers, and Rollo May. Maslow founded the psychology department at Brandeis University in 1951 with a strong humanistic orientation even before the movement was thus named. Originally working within experimental psychology, Maslow (1954), developed a research program and subsequent humanistic theory of motivation. He argued that people are motivated not only reactively by the "deficiency needs" with which psychology had hitherto been concerned, but also proactively by "being needs," ultimately including such motives as self-actualization.Rogers (1951) sought ways to facilitate clients' yearning for self-actualization and fully-functioning living, especially via person-centered therapy and group work. He was one of the first researchers to study psychotherapy process using tape-recordings and transcripts, and he and his students also made extensive use of Q-sorts to study self-concept and change. He explored the necessary conditions for therapeutic progress and emphasized congruence, presence, and acceptance on the part of the therapist.May, Angel, and Ellenberger (1958) built a bridge from interpersonal psychoanalysis and European existentialism and phenomenology, having been influenced by Harry Stack Sullivan, Ludwig Binswanger, and Medard Boss. May's books integrated creativity, the arts, mythology and the humanities with psychology, and encompassed the tragic view of life and the daimonic forces. Charlotte Bühler, Erich Fromm, and Viktor Frankl also contributed European perspectives to this stream, including a concern for values in psychotherapy, human development over the whole course of human life, humanistic psychoanalysis, social issues, love, transcendence of evil, and the search for meaning.In the 1960s many isolated voices began to gather momentum and form a critique of American culture and consciousness, and to form the basis of a new approach to psychology. Massive cultural changes were sweeping through America. That larger movement was an expression of a society eager to move beyond the alienating, bland conformity, embedded presuppositions, and prejudices that had characterized the 1950s return to "normalcy" after World War II. In psychology, adjustment models were challenged by visions of growth, and the human potential movement emerged. T-groups, sensitivity training, human relations training, and encounter groups became popular. The goal was greater awareness of one's own actual experience in the moment and authentic engagement with others, goals not well-served by academic psychology, clinical psychology, or the culture in general. Growth centers sprang up across the country, offering a profusion of workshops and techniques, such as transactional analysis, sensory awareness, Gestalt encounter, body work, meditation, yoga, massage therapy, and psychosynthesis. The best known of these was Esalen Institute, founded in Big Sur, California in 1964, which continues tothis day. Begun as a site for seminars, it featured not only psychologists such as Rollo May, Abraham Maslow, and Carl Rogers, but also scholars from other disciplines such as Arnold Toynbee, Paul Tillich, Gregory Bateson and Alan Watts.These developments in the culture and in "pop psychology" paralleled changes in clinical and academic domains. Existential and phenomenological trends in continental psychiatry affected the Anglo-American sphere through the work of R. D. Laing and his British colleagues. His trenchant critique of the prevailing medical model's reductionistic and pathological view of schizophrenic patients began a revisioning of even psychotic processes as meaningful growth-seeking experiencing. Various American psychiatrists also contributed to the elaboration of this alternative, most notably John Perry and Thomas Szasz. At the same time, Gestalt therapy was developed and popularized especially by Fritz Perls.Meanwhile, from the academic side a rising tide of theory and research focused attention on this nonreductive, holistic view of the person. As the 1960s unfolded, new books by Rogers (1961, 1969), Maslow (1962, 1964, 1965, 1966), and May (1967, 1969) were enormously influential in this more receptive era. May pointed out that if we are to study and understand human beings, we need a human model. He advocated a science of persons, by which he meant a theory which would enable us to understand and clarify the specific, distinguishing characteristics of human beings. Many new voices also now began to be raised. Amedeo Giorgi (later Division 32 president in 1987-1988) criticized experimental psychology's reductionism, and argued for a phenomenologically based methodology that could support a more authentically human science of psychology (Giorgi, 1965, 1966, 1970). Giorgi argued that psychology has the responsibility to investigatethe full range of behavior and experience of people in such a way that the aims of rigorous science are fulfilled, but that these aims should not be implemented primarily in terms of the criteria of the natural sciences.As an organized movement, humanistic psychology grew out of a series of meetings in the late 1950s initiated by Abraham Maslow and Clark Moustakas and including Carl Rogers, all APA members. They explored themes such as the nature of the self, self-actualization, health, creativity, being, becoming, individuation, and meaning. Building on these meetings, in 1961 an organizing committee including Anthony Sutich launched the Journal of Humanistic Psychology (JHP). Its early editorial board included many well-known scholars such as Andras Angyal, Erich Fromm, Kurt Goldstein, Rollo May, Clark Moustakas, and Lewis Mumford. Maslow had compiled a mailing list of colleagues to whom he sent his papers which conventional journals would not publish, and this was used to begin the promotion of JHP (deCarvalho, 1990).The new journal's success in coalescing a responsive subscriber base quickly convinced its founders that a professional association could also meet a need. With the assistance of James Bugental, who served as its first president pro tem, and a grant arranged by Gordon Allport, the inaugural meeting of the Association for Humanistic Psychology (AHP) was held in Philadelphia in 1963. Among the 75 attendees were many who would later play prominent leadership roles in this movement. (For a summary of this meeting see deCarvahlo, 1991, pp. 10-11.)In 1963 James Bugental published a foundational article, "Humanistic Psychology: A New Breakthrough," in the American Psychologist which was adopted by AHP as a basic statement of its own orientation. This statement was amplified in Bugental's 1964 article, "The Third Force in Psychology" inthe Journal of Humanistic Psychology and appears, in the following slightly amplified version, in each issue of JHP.Five Basic Postulates of Humanistic Psychology1. Human beings, as human, are more than merely the sum of theirparts. They cannot be reduced to component parts or functions.2. Human beings exist in a uniquely human context, as well as in acosmic ecology.3. Human beings are aware and aware of being aware—i.e., they areconscious. Human consciousness potentially includes anawareness of oneself in the context of other people and thecosmos.4. Human beings have some choice, and with that, responsibility.5. Human beings are intentional, aim at goals, are aware that theycause future events, and seek meaning, value and creativity.(Bugental, 1964, pp. 19-25)The second AHP meeting took place in Los Angeles in September 1964, with about 200 attendees. As Bugental observed, this group already included the four major subgroups that have characterized and sometimes strained the association ever since: therapists, social/political activists, academic theorists and researchers, and "touchy feely" personal growth seekers (deCarvalho, 1991, 1992).To develop the philosophy, themes and direction of the Association for Humanistic Psychology and humanistic psychology theory, The Old Saybrook Conference was convened in 1964 at a Connecticut country inn. It was an invitational conference sponsored by AHP, financed by the Hazen Foundation, and hosted by Wesleyan University under the chairmanship of Robert Knapp. Leading figures in the psychology of personality and in the humanisticdisciplines participated: Gordon Allport, George Kelly, Clark Moustakas, Gardner Murphy, Henry Murray, and Robert White of the founding generation; Charlotte Bühler, representing a European tradition of research labeled "life-span development," Jacques Barzun and Rene Dubos as humanists from literature and biological science, and James Bugental, Abraham Maslow, Rollo May, and Carl Rogers, who became the intellectual leaders of the movement. These founders did not intend to neglect scientific aspirations; rather, they sought to influence and correct the positivistic bias of psychological science as it then stood. The titles of some of the papers indicate the focus of the conference: "Some Thoughts Regarding the Current Philosophy of the Behavioral Sciences" by Carl Rogers, "Intentionality, the Heart of Human Will" by Rollo May, "Psychology: Natural Science or Humanistic Discipline?" by Edward Joseph Shoben, and "Humanistic Science and Transcendent Experiences" by Abraham Maslow.In addition to the Journal of Humanistic Psychology, the Association for Humanistic Psychology, and the Old Saybrook Conference, the subsequent years also saw the founding of graduate programs in humanistic psychology. Masters' programs in humanistic psychology were begun in 1966 at Sonoma State University (then Sonoma State College), and in 1969 at the State University of West Georgia (then West Georgia College). An M.A. program in existential-phenomenological psychology was created at Duquesne University in 1959, and a Ph.D. program was added in 1962. Several free-standing institutes also initiated humanistic graduate programs. John F. Kennedy University and the Union Institute, both begun in 1964, and the California Institute of Integral Studies in 1968 were among the first. In 1971 the Association for Humanistic Psychology created the Humanistic Psychology Institute (now known as Saybrook Graduate School, named afterthe famous conference). These early programs, still continuing, have since been joined by many others. Thirty-seven are listed in the current Directory of Graduate Programs in Humanistic-Transpersonal Psychology in North America (Arons, 1996). Some of these have focused on synthesizing humanistic scholarship with eastern philosophies such as Hinduism and Buddhism (the best known of these are the California Institute for Integral Studies, John F. Kennedy University, the Institute for Transpersonal Psychology, and Naropa Institute). Faculty members from these graduate programs have been active in Division 32 and many, especially from State University of West Georgia and Saybrook Graduate School, have served as its president.The Founding of Division 32: Ambivalence and Collaboration During the 1960s the primary organizational forum for the burgeoning humanistic movement was the Association for Humanistic Psychology (AHP), which had become an organization of 6,600 thousand members. As a protest movement against the mainstream approaches in psychology, this alternative venue outside of APA seemed most appropriate. However, as the momentum of change during the 1960s continued, the mainstream also began to open up to much of this new thinking. Abraham Maslow was elected president of the American Psychological Association in 1968. (Rogers had been president in 1947, and later Stanley Graham and Brewster Smith, two Division 32 presidents, also served as APA presidents.) Eventually, a group of psychologists within APA decided to pursue the organization of an APA division devoted to humanistic psychology.This effort was spearheaded by Don Gibbons, then a faculty member at West Georgia College. In order to propose a new division, the signatureson a petition to APA of 1% of APA's existing membership were required (approximately 275 at that time). In January 1971, Gibbons wrote to John Levy, the executive director of AHP, seeking his support in soliciting these signatories from APA members who belonged to AHP. Many members of AHP were also members of APA, so it was evident that the two groups would have a significant overlapping membership. As Gibbons wrote in that January 12, 1971 letter: "We would like to see it set up in such a way as to facilitate communication between the A.P.A. and all areas of the humanistic movement. In particular, we would like to see the new division maintain the closest possible degree of collaboration with A.H.P." In the end, 374 members of APA petitioned for the proposed division. As a result, the APA Council of Representatives, after hearing receiving affirmation from the existing divisions of APA, confirmed and made official the new Division of Humanistic Psychology.This prospect of another humanistic organization raised concern on the part of some that it would dilute the movement (Arons, personal communication, June 6, 1998). The proponents of the proposed division, however, were in any case determined to proceed, and viewed the eventual formation of a Division of Humanistic Psychology within the APA as inevitable, given the continuing rapid growth of humanistic psychology at that time. Though still wary, previously opposed members of AHP who also belonged to APA chose to help make the proposed division the best it could be, and gathered at the official organizational meeting scheduled by Gibbons during the 1971 APA convention (Harari, personal communication, June 26, 1998). For unknown reasons, Gibbons himself did not attend the meeting. Spontaneously, a group of individuals occupied the dais and took charge of the meeting.Several people presented the case for a new division. Albert Ellis spoke eloquently for its value in giving a voice within APA to humanistic psychology. Fred Massarik indicated that he had been originally opposed to the proposed division, but now supported it. It was proposed that a steering committee of 11 be elected who would constitute an acting executive board during the coming year, to establish by-laws and a statement of purpose.As Harari described this first meeting in his letter to the new division's members:On Saturday, September 4, 1971 an organizing meeting washeld for the Division of Humanistic Psychology of APA during therecent APA meetings held in Washington, D.C. Fifty-sevenpersons attended the organizing meeting and together withoriginal petitioners for the formation of the new Division, as wellas other interested members and fellows, became the chartermembers of the new Division. In the absence of the originallyscheduled chairperson, Don Gibbons of West Georgia College,Albert Ellis was appointed Chairman of the meeting and CarmiHarari was appointed Recording Secretary....Several signers ofthe original petition were present in the room and assisted in theconduct of the meeting, together with the expert consultingassistance of Jane Hildreth, representing APA CentralOffice....Serving as Presiding Officers for the organizing meetingwere Albert Ellis, Stanley Graham, Carmi Harari, Fred Massarik,Denis O'Donovan and Everett Shostrom. (Harari, 1971)The first meeting of the acting executive board took place immediately following the organizational meeting of the new division. Officers were elected, with Harari chosen as acting president, Graham as acting treasurer,Ellis as acting council representative, and Shostrom and Massarik as co-chairs of the next convention's program. Three other decisions, all of which would be subsequently challenged and changed, were made: the first program would be on an invitational basis; dues were set at $3.00; and Fellows, Members, and Associates of APA would be eligible for division membership on an equal basis with no classes of membership in the division.The Early Years: Growth and InnovationThe following year, 1972, saw the usual development and application of those processes by which a new organization becomes normalized including membership, governance, programs, and publications.. What was reflective of the spirit of Division 32, however, was the open, explorative approach to these features, which were handled in innovative ways. MembershipA highly successful recruitment of new members, by Barton Knapp as acting membership chair, brought in about 300 new applications during the Division's first year, almost doubling the membership total. By January 1, 1973, the total was 647; in 1974 it was 784. By 1975, it topped 900, and by 1976 it was more than a thousand. In 1977 it reached 1150, the highest level where it then stabilized for the next few years.During the 1973-74 year, the membership chair, Nora Weckler, conducted a survey of members, and itemized their major fields of involvement. Most heavily represented was counseling psychology. Clinical and educational psychologists were also strongly represented, followed by psychotherapy, experimental, social, industrial, and developmental psychologists. Smaller numbers included: engineering, environmental,perception, rehabilitation, and philosophical psychologists. Weckler also noted that the Division's first international members came from Venezuela, Japan, and India. She also itemized reasons given for joining the Division. These included:to have closer contact with others of similar interests; to learnmore about the humanistic approach....a desire for personal andprofessional growth and training....to learn how psychology canhelp people lead a more fulfilling life....to support the philosophyof Division 32....because of dissatisfaction with AHP's anti-intellectual and anti-scientific attitude....an appreciation of theblending of both art and science....a desire to learn more of whatthe Division was doing....an interest in the unresolved theoreticaland philosophical problems of humanistic psychology....with thehope that the Division will further develop theory and researchfollowing an existential-phenomenological approach. (NoraWeckler, Membership Chair Report, 1971)In the following year's membership survey (1974-75), Weckler turned up mostly continuations of these trends. Members now also came from Great Britain, Canada, Guam, and Puerto Rico. Interest areas covered almost every subfield of psychology, with clinical psychology being the most heavily represented, counseling a close second, and educational psychology third. Social psychology, developmental psychology, rehabilitation psychology, speech and communication psychology, and pastoral psychology were also prominently mentioned.At that point in its history, Division 32 defined its mission as follows in an undated statement:Humanistic psychology aims to be faithful to the full range of humanexperience. Its foundations include philosophical humanism,existentialism, and phenomenology. In the science and profession ofpsychology, humanistic psychology seeks to develop systematic andrigorous methods of studying human beings, and to heal thefragmentary character of contemporary psychology through an evermore comprehensive and integrative approach. Humanisticpsychologists are particularly sensitive to uniquely human dimensions, such as experiences of creativity and transcendence, and to the quality of human welfare. Accordingly, humanistic psychology aims especially at contributing to psychotherapy, education, theory, philosophy ofpsychology, research methodology, organization and management and social responsibility and change.GovernanceIn early 1972 drafts of the new Division's by-laws were circulated to John Levy, the executive director at AHP, to Jane Hildreth at APA Central Office, and to the Division 32 members for their comments. The purpose of the Division, as stated in these first by-laws, was to apply the concepts, theories, and philosophy of humanistic psychology to research, education, and professional applications of scientific psychology.Only two aspects of the draft by-laws were seen as problematic. Levy pointed out that requiring decisions to be approved at the annual business meeting might result in a small turnout producing unrepresentative results. Mail-in balloting was then also included as a decision-making tool. Levy also questioned the unwieldy large size of the executive board, which included nine at-large members. (This number was later reduced to six.) Hildreth, at APA, noted (in her letter to Gloria Gottsegen, March 7, 1972) that theDivision's desire to have only one class of members, while laudable, conflicted with APA by-laws that prohibit a person from holding higher member status in a division than he/she does in APA. In the case of APA's three classes of membership (Fellow, Member, and Associate), it would be no problem to consider APA Fellows to be Members of Division 32, but Associates in APA could not be promoted to Member status in the Division. This dilemma was resolved, however, by allowing APA Associates to enjoy full membership status in the Division as members who could vote and hold office on an equal basis, with the sole exception that they could not vote for the Council Representative position (as that voting eligibility is part of APA's own by-laws). Division elections would henceforth require the Division secretary to count the ballots of Division members who, as Associates in APA, were not eligible to vote in APA elections, and whose ballots would therefore not be sent to APA. This added complication was seen as well worthwhile, to be able to establish a more egalitarian collegium of members, of whom about 20% were only Associate members of APA.As a result of the initial rapid growth in membership, along with a very positive response to Harari's first appeal of support in the APA apportionment balloting, the new Division was awarded two seats on APA's Council of Representatives. Following a call for nominations, the Division's first election was held, in 1972, to select its first actual (rather than acting) officers. Carmi Harari was elected president, Everett Shostrom president-elect, Gloria Gottsegen secretary, Barry Crown treasurer, Fred Massarik and Albert Ellis council representatives. Members-at-large of the executive board were also elected, to serve staggered terms. These included: David Bakan, Elizabeth Mintz, Joen Fagen, Robert Strom, Leonard Blank, Lawrence LeShan, James Klee, Janette Rainwater and Barton Knapp.When Shostrom became president he presented the executive board with a silver oil can engraved with the inscription, "APA Division 32 President's Actualizing Oil Can" on which he had inscribed the names of the first two division presidents (Harari and Shostrom). He recounted the story of the Wizard of Oz. The straw man, the tin man and the cowardly lion were seeking from an outside authority qualities they already possessed within themselves. Opening to these inner qualities is a prime message of humanistic psychology. The oil can used by the tin man to lubricate his joints became a ritual reminder of this message as it passes, each name added, from outgoing to incoming presidents.Beginning with the first elected executive board meeting, in 1972 during the APA convention in Honolulu, innovations and changes were typical. Convention programming was changed from being exclusively invitational. It was decided to allot only 50% to invited symposia and 50% to proposals solicited from members. A newsletter was inaugurated, with Alvin Manaster appointed as its first editor, and a Social Responsibility Committee was formed with James Klee as its first chair. A proposal by Robert Strom to hold a mid-year executive board meeting was also accepted. It was also decided to include a regular column about Division 32 in AHP's newsletter, so as to continue the hoped-for collaboration between the two groups.The election of 1974 featured a problem and creative resolution. The balloting for the position of president-elect resulted in a tie vote between Myron Arons and Stanley Graham. With the concurrence of the two candidates, President Shostrom flipped a coin to determine the results. It was agreed that, since Stanley Graham won the toss, he would function as President-elect for the 1974-1975 term and that he would function as。

Chern-Simons理论

$\textbf{外微分形式}$
实流形$M$上$U\subset M$为一稠密开集，令其足够小使得存在有m维局域坐标满足
\[
M\supset U\ni x\leftrightarrow\widetilde{x}\triangleq (x^1,...,x^m)\in\mathbb{R}^m
$\rho_{i_1...i_r}$为交错张量；
坐标变换后得
\[
y=y(x):df=(\partial\widetilde{f}/\partial x^i)dx^i=(\partial\widetilde{f}/\partial y^i ) (\partial y^i/\partial x^i)dx^i=(\partial\widetilde{f}/\partial y^i ) dy^i
其中曲率张量定义为：$F=dA+A\wedge A$
通常的Chern–Simons $\omega_{2k-1}$形式由以下方式给出：$d\omega_{2k-1}=\text{Tr}(F^k)$
其中由楔积定义，等式右边正比于联络的第陈类。
一般地，由定义可知Chern–Simons p-形式中的是任意奇数$2k-1$。（可参考规范理论的定义）若$M$是平庸$2k-1$维流形（i.e.三维可定向流形），那么存在映射 $s: M\rightarrow P(M)$；并且从$s^{*}\omega_{2k-1}$在p维流形上的积分是整体几何不变量，且是模增加一整数的规范不变量。
由它（3-形式）可定义Chern–Simons理论的作用量。陈省身与James Harris Simons于1974年合作发表了一篇历史性文章，文中提出了 Chern–Simons理论。$M$为Riemann流形，其联络$A\in \Omega^1(P(M),\mathfrak{g}l(n))$是标架丛$P(M)$上的1-形式Lie代数。给定一流形与1-形式Lie代数，$A$为上面的向量场。可由此定义一族p-形式。

Phys LettersB.286,118

(3)
ቤተ መጻሕፍቲ ባይዱ
(4)
C
C'
where v[C, C'] is the number of right-handed minus the number of left-handed intersections of C and C'. (A right-handed intersection occurs when, if we move along the positive direction of C, C' crosses from right to left. ) Thus, the commutator gives a representation of the intersection form for Wilson loops. For closed curves C and C', v [ C, C' ] is a topological invariant and if either C or C' is contractible, u [ C, C' ] must vanish. Therefore, there is a nontrivial commutator only for homologically nontrivial curves. If%, fJj,j= 1..... g, are a canonical set of closed curves on Y.g generating its first homology group then v[a;, aj] = u[[3;, [3j] =0, v[ct;, [3j] =d;j. Upon imposition of the constraint (2) the integrals of A over the one-cycles a;, ~i are the only remaining degrees of freedom and, modulo the remaining symmetry under large gauge transformations, they form the reduced phase space [ 2 ]. It is the property (4), that the symplectic structure gives the intersection form for loops on E g, which we shall discover on the lattice as a consequence of lattice gauge invariance and locality. We work in continuum time and a square spatial lattice with spacing I. We begin by fixing some notation. The forward and backward shift operators are S ; f ( x ) = f (x + [), $7 ~f(x) = f ( x - {), respectively, and forward and backward difference operators are d i f ( x ) = f ( x + f) - f ( x ) , d;= S i - 1, a j ( x ) = f ( x ) - f ( x - [), a; = 1 - s7 ~= s7 ~d;. Summation by parts on a lattice takes the form (neglecting surface terms ) Y x f ( x ) d;g (x) = - Yx a;f(x) g (x) by virtue of the lattice Leibniz rule d;(fg) = f d ; g + d J S;g=fd;g+ S; (aorg) (no sum on i). The components A,(x) of the gauge field are realvalued functions on the links specified by the pair [x, [], Ao is a function on lattice sites, the magnetic field B (x) = d iA2(x) - d z A l (X) is a function on plaquettes where x labels the plaquette with corners x, x + L x + T + 2, x + 2 , and the electric field Fo;=e]i- de4o is a function on links. A gauge invariant, local, nondegenerate Chern-Simons term was found in ref. [ 11 ] :

``Bare'' Effective Mass in Finite Sized $nu = 12$ Systems

We will be doing ﬁnite sized calculations on the torus, and for this it is convenient to equivalently deﬁne the bosonic Laughlin state as the ground state of bosons at ν = 1/2 interacting with a hard-core repulsive potential. Then in terms of this bosonic Laughlin state, we can deﬁne a fermionic state for the cluster {ki }N i=1 as Ψ({ki }N i=1 ) = det exp iki · Rj |ΨL (ν = 1/2)
0 N Let us denote the collection of momenta for the relaxed ”most circular” cluster by {ki }i=1
and let {ki}N i=1 depict an excited cluster (see ﬁgure 1 for an example when N = 9). Then the energy of the relaxed conﬁguration is (let H be the Hamiltonian for fermions with coulomb interaction, for example)
ij
(2)
Note that this wavefunction has the correct statistics (fermionic) and ﬁlling factor. It has been shown elsewhere [3] that for any given set of periodic boundary conditions, the choice of {k i }N i=1 that gives the ”most circular” compact conﬁguration possible yields a wavefunction that is almost exactly the ground state for fermions interacting with coulomb interactions [3]. For example, the overlap between two arbitrary states is no more than a few percent, while the fermionic slater determinant state (equation 2) for the ”most circular” cluster has 2

【高一学习指导】[数学思维拓展]2002年诺贝尔经济学奖

【高一学习指导】[数学思维拓展]2002年诺贝尔经济学奖瑞典斯德哥尔摩当地时间10月8日15：30（北京时间8日21：30），瑞典皇家科学院宣布，将当年诺贝尔经济学奖授予美国普林斯顿大学的丹尼尔-卡恩曼（danielkahneman拥有美国和以色列双重国籍）和美国乔治-梅森大学的弗农-史密斯（vernonl.smith）。

瑞典皇家科学院称，丹尼尔-卡恩曼“将来自心理研究领域的综合洞察力应用在了经济学当中，尤其是在不确定情况下的人为判断和决策方面作出了突出贡献。

”弗农-史密斯“建立了实验室实验，并将其作为一种工具应用于经验经济分析中，尤其是在选择性市场机制的研究中获得了突出成就。

”丹尼尔-卡恩曼（danielkahneman）个人简历：丹尼尔-卡恩曼1934年出生于以色列的特拉维夫高中历史，今年68岁，具有美国和以色列的双重国籍。

他于1961年赢得了加州大学伯克利分校的博士学位，从1993年已经开始出任普林斯顿大学心理学教授和公共关系学教授。

弗农-史密斯（vernonl.smith）简历：弗农-史密斯1927年出生于美国堪萨斯州维芝塔，今年75岁。

他于1955年获得哈佛大学博士学位，自2001年开始担任乔治-梅森大学的经济学和法律教授。

他们将互动1000万瑞典克朗（约合100万美元）的奖金。

诺贝尔经济学奖并非诺贝尔遗嘱中提到的五大奖励领域之一，是由瑞典银行在1968年为纪念诺贝尔而增设，全称应为“纪念阿尔弗雷德-诺贝尔瑞典银行经济学奖”，其评选标准与其它奖项是相同的，获奖者由瑞典皇家科学院评选，1969年第一次颁奖，由挪威人弗里希和荷兰人丁伯根共同获得，美国经济学家萨缪尔森、弗里德曼等人均获得过此奖。

2001年的诺贝尔经济学奖就是三位美国人：乔治-阿克洛夫、麦克尔-斯宾塞和约瑟夫-斯蒂格利茨。

他们因为在现代信息经济学研究领域所作的突出贡献而得奖。

Duality Equivalence Between Self-Dual And Topologically Massive Non-Abelian Models

a rXiv:h ep-th/014115v28M a y21Duality Equivalence Between Self-Dual And Topologically Massive Non-Abelian Models A.Ilha and C.Wotzasek Instituto de F´ısica,Universidade Federal do Rio de Janeiro,Caixa Postal 68528,21945Rio de Janeiro,RJ,Brazil.(February 7,2008)The non-abelian version of the self-dual model proposed by Townsend,Pilch and van Nieuwenhuizen presents some well known diﬃculties not found in the abelian case,such as well deﬁned duality operation leading to self-duality and dual equivalence with the Yang-Mills-Chern-Simons theory,for the full range of the coupling constant.These questions are tackled in this work using a distinct gauge lifting technique that is alternative to the master action approach ﬁrst proposed by Deser and Jackiw.The master action,which has proved useful in exhibiting the dual equivalence between theories in diverse dimensions,runs into trouble when dealing with the non-abelian case apart from the weak coupling regime.This new dualization technique on the other hand,is insensitive of the non-abelian character of the theory and generalize straightforwardly from the abelian case.It also leads,in a simple manner,to the dual equivalence for the case of couplings with dynamical fermionic matter ﬁelds.As an application,we discuss the consequences of this dual equivalence in the context of 3D non-abelian bosonization.I.INTRODUCTIONThe bosonization technique that expresses a theory of interacting fermions in terms of free bosons provides a powerful non-perturbative tool for investigations in diﬀerent areas of theoretical physics with practical applications [1].In two-dimensions these ideas have been extended in an interpolating representation of bosons and fermions which clearly reveals the dual equivalence character of these representations[2].In spite of some diﬃculties,the bosonization program has been extended to higher dimensions[3,4].In particular the2+1dimensional massive Thirring model(MTM)has been bosonized to a free vectorial theory in the leading order of the inverse mass ing the well known equivalence between the self-dual[5] and the topologically massive models[6]proved by Deser and Jackiw[7]through the master action approach[8],a correspondence has been established between the partition functions for the MTM and the Maxwell-Chern-Simons (MCS)theories[9].The situation for the case of fermions carrying non-abelian charges,however,is less understood due to a lack of equivalence between these vectorial models,which has only been established for the weak coupling regime [10].As critically observed in[11]and[12],the use of master actions in this situation is ineﬀective for establishing dual equivalences.In this paper we intend toﬁll up this gap.We propose a new technique to perform duality mappings for vectorial models in any dimensions that is alternative to the master action approach.It is based on the traditional idea of a local lifting of a global symmetry and may be realized by an iterative embedding of Noether counter terms.This technique was originally explored in the context of the soldering formalism[13,14]and is exploited here since it seems to be the most appropriate technique for non-abelian generalization of the dual mapping concept.Using the gauge embedding idea,we clearly show the dual equivalence between the non-abelian self-dual and the Yang-Mills-Chern-Simons models,extending the proof proposed by Deser and Jackiw in the abelian domain.These results have consequences for the bosonization identities from the massive Thirring model into the topologically massive model,which are considered here,and also allows for the extension of the fusion of the self-dual massive modes[14]for the non-abelian case[15].We also discuss the case where charged dynamical fermions are coupled to the vector bosons.For fermions carrying a global U(1)charge we reproduce the result of[16]but the result for the non-abelian generalization is new.The technique of local gauge lifting is developed in section II through speciﬁc examples.In section III we show how the gauge embedding idea solves the problem of non-abelian dual equivalence.For completeness weﬁrst discuss the abelian case showing how the well known results are easily reproduced.The case of dual equivalence between the SD and the MCS when dynamical fermionﬁelds are coupled to the gaugeﬁelds is also considered,both in the abelian and in the non-abelian cases.The remaining sections are dedicated to explore this result in the non-abelian bosonization program and to present our conclusions.II.NOETHER GAUGE EMBEDDING METHODRecently there has been a number of papers examining the existence of gauge invariances in systems with second class constraints[17].Basically this involves disclosing,using the language of constraints,hidden gauge symmetries in such systems.This situation may be of usefulness since one can consider the non-invariant model as the gauge ﬁxed version of a gauge theory.By doing so it has sometimes been possible to obtain a deeper and more illuminating interpretation of these systems.Such hidden symmetries may be revealed by a direct construction of a gauge invariant theory out of a non-invariant one[18].The former reverts to the latter under certain gaugeﬁxing conditions.The associate gauge theory is therefore to be considered as the embedded one.The advantage in having a gauge theory lies in the fact that the underlying gauge invariant theory allows us to establish a chain of equivalence among diﬀerent models by choosing diﬀerent gaugeﬁxing conditions.In this section we shall review a diﬀerent technique to achieve this goal:the iterative Noether gauging procedure. For pedagogical reasons,we develop simple illustrations making use of scalarﬁeld theories living in a Minkowski space-time of dimension two.This will allow us to discuss some subtle technical details of this method,regarding the connection between the implementing symmetries and the Noether currents,which are necessary for its application in the2+1dimensional self-dual model.The important point to stress in this review of the iterative Noether procedure is its ability to implement speciﬁc symmetries leading to distinct models.To avoid unnecessary complications let us consider the case of a free two dimensional scalarﬁeld theory,S(0)=1and choose to gauge either the axial shift,(i)ϕ→ϕ+ǫ,(2) or the conformal symmetry,(ii)ϕ→ϕ+ǫ∂−ϕ,(3) (∂0±∂1)andǫis a global parameter.In theﬁrst case it is simple to identify the Noether current as, where∂±=12Jµ=∂µϕ,(4) which comes from the variation of the scalarﬁeld actionδS(0)= d2x Jµ∂µǫ,(5) which is non-vanishing ifǫis lifted to its local version.To compensate for this non-vanishing result we introduce a counter-term together with an ancillary gaugeﬁeld Bµ(also called as compensatoryﬁeld)as,S(1)=S(0)− d2x JµBµ,(6) such that its variation reads,δS(1)=− d2x BµδJµ,(7) which is achieved if Bµtransforms as a vectorﬁeld simultaneously with(2).Introducing an extra counter-term as,S(2)=S(1)+1III.DUAL EQUIV ALENCE OF SD AND MCS THEORIESIn this section we discuss the application of the gauge invariant embedding to show the dual equivalence between the SD model with the MCS theory both abelian and non-abelian including the coupling with charged dynamical matter ﬁelds.As mentioned in the introduction this has the advantage of possessing a straightforward extension to the non-abelian case for all values of the coupling constant.Let us recall that the essential properties manifested by the three dimensional self-dual theory such as parity breaking and anomalous spin,are basically connected to the presence of the topological and gauge invariant Chern-Simons term.The abelianself-dual model for vector ﬁelds was ﬁrst introduced by Townsend,Pilch and van Nieuwenhuizen[5]through the following action,S χ[f ]= d 3x χ2f µf µ ,(15)where the signature of the topological terms is dictated by χ=±1and the mass parameter m is inserted for dimensional reasons.Here the Lorentz indices are represented by greek letters taking their usual values as µ,ν,λ=0,1,2.The gauge invariant combination of a Chern-Simons term with a Maxwell actionS (MCS )= d 3x 12mǫµνλf µ∂νf λ ,(16)is the topologically massive theory,which is known to be equivalent [7]to the self-dual model (15).f µνis the usual Maxwell ﬁeld strength,f µν≡∂µf ν−∂νf µ.(17)The non-abelian version of the vector self-dual model (15),which is our main concern in this work,is given byS χ= d 3x tr −14mǫµνλ F µνF λ−24m 2F µνF µν+χ3F µF νF λ ,(20)only in the weak coupling limit g →0so that the Yang-Mills term eﬀectively vanishes 1.To study the dual equivalence of (18)and (20)for all coupling regimes and the consequences over the bosonization program is main contribution of this work.Next we analyze the dualization procedure in the massive spin one self-dual theories using the Noether gauging procedure.To begin with,it is useful to clarify the meaning of the self duality inherent in the action (15).The equation of motion in the absence of sources is given by,f µ=χ1Here we are using the bosonization nomenclature that relates the Thirring model coupling constant g 2with the inverse mass of the vector model;see discussion after Eq.(62)∂µfµ=0,2+m2 fµ=0.(22) From(21)and(22)we see that there is only one massive excitation whose value is m.Aﬁeld dual to fµis deﬁned as,⋆fµ=1mǫµνλ∂ν⋆fλ=fµ,(24)obtained by exploiting(22),thereby validating the deﬁnition of the dualﬁbining these results with(21),we conclude that,fµ=χ⋆fµ.(25) Hence,depending on the signature ofχ,the theory will correspond to a self-dual or an anti self-dual model.To prove the exact equivalence between the self-dual model and the Maxwell Chern-Simons theory,we start with the zeroth-iterated action(15)which is non-invariant by gauge transformations of the basic vectorﬁeld fµ.To construct from it an abelian gauge model,we have to consider the gauging of the following symmetry,δfµ=∂µξ,(26) whereξis an inﬁnitesimal local parameter.Under such transformations,the action(15)change as,δSχ= d3x Jµ(f)∂µξ,(27) where the Noether currents are deﬁned by,Jµ(f)≡−fµ+χ2BµBµ ,(32)which is invariant under the combined gauge transformations(26)and(29).The gauging of the U(1)symmetry is complete.To return to a description in terms of the original variables,the auxiliary vectorﬁeld is eliminated from (32)by using the equation of motion,Bµ=−Jµ.(33)Note that taking variations on both sides of this equation and using the gauge invariance of the Chern-Simons form we obtain consistency with the conditionδfµ=δBµ.It is now crucial to note that,by using the explicit structures for the currents,the above action(32)forms a gauge invariant combination expressed by the action(16)which is the Maxwell Chern-Simons theory.Our goal has been achieved.The iterative Noether dualization procedure has precisely incorporated the abelian gauge symmetries in the self-dual model to yield the gauge invariant Maxwell Chern-Simons theory.The free case considered above can also be extended to couplings with external,ﬁeld-independent sources.To illustrate this point,we consider a coupling between dynamical U(1)charged fermions and self-dual vector bosons [16].In the abelian case,this model is written asS[f,ψ]=Sχ[f]+ d3x −e fµJµ+¯ψ(i∂/−M)ψ ,(34)where Jµ=¯ψγµψand M is the fermionic mass.Sχis the self-dual action(15).The Noether current associated with this action isχKµ=−fµ+BµBµ .(36)2After the elimination of Bµthrough its equations of motion,we get ourﬁnal theory,S=S(MCS)+ d3x e2JµJµ+eχfµGµ+L D ,(37) where S(MCS)is the Maxwell Chern-Simons action(16)and L D is the free Dirac Lagrangian.Here Gµ=1ǫµνλ(∂µ+Fµ) Fν,(39)mwhere the operator inside the square brackets in the right-hand side acts on the basicﬁeld Fνdeﬁning⋆Fλas the dual of Fν.Repeating this operation,and using the equations of motion obtained by varying(18)with respect to FλχFλ=with the Noether currents being deﬁned as,Jµ=−Fµ+χ2δ(JµJµ)−δ(JµBµ)−JµδBµ ,(45) where we have used the following transformation rule for the gaugingﬁeld,δFµ=−δBµ−δJµ.(46) This prompt us to deﬁne the following second iterated action,S(2)=Sχ+ d3x tr 14mǫµνλ FµνFλ−22BµBµ (47) which is gauge invariant after noticing that the transformation rule(46)ﬁxes the Bµﬁeld asBµ=−χ2m ǫµνλFµνJλ+e2Bosonization was developed in the context of the two-dimensional scalarﬁeld theory and has been one of the main tools available to investigate the non-perturbative behavior of some interactiveﬁeld theories[1].For some time this concept was thought to be an exclusive property of two-dimensional space-times where spin is absent and one cannot distinguish between bosons and fermions.It was only recently that this powerful technique were extended to higher dimensional space-times[24,25][9,26].The bosonization mapping in D=3,ﬁrst discussed by Polyakov[27],shows that this is a relevant issue in the context of transmutation of spin and statistics in three dimensions.The equivalence of the three dimensional eﬀective electromagnetic action of the CP1model with a charged massive fermion to lowest order in inverse(fermion)mass has been proposed by Deser and Redlich[28].Using their results bosonization was extended to three dimensions in the1/m expansion[9].These endeavor has led to promising results in diverse areas such as,for instance,the understanding of the universal behavior of the Hall conductance in interactive fermion systems[29].For higher dimensions,due to the absence of an operator mapping a la Mandelstan,the situation is more complicate and even the bosonization identities extracted from these procedures relating the fermionic current with the bosonic topological current is a consequence of a non-trivial current algebra.Moreover,contrary to the two dimensional case, in dimensions higher than two there are no exact results with the exception of the current mapping[22,23].Besides, while the two-dimensional fermionic determinant can be exactly computed,here it is neither exact nor complete, having a non-local structure.However,for the large mass limit in the one-loop of perturbative evaluation,a local expression materializes.This procedure,is in a sense,opposite to what is done in1+1dimensions where bosonization is a set of operator identities valid at length scales short compared with the Compton wavelength of the fermions while in D=3only the long distance regime is considered.In this section we review how the low energy sector of a theory of massive self-interacting,G-charged fermions,the massive Thirring Model in2+1dimensions,can be bosonized into a gauge theory,the Yang-Mills-Chern-Simons gauge theory thanks to the results of the preceeding section.A.The Non-Abelian MappingIn the sequence we investigate the problem of identifying a bosonic equivalent of a three dimensional theory of self-interacting fermions with symmetry group G and show how it is possible to bosonize the low-energy regime of the theory.We follow the same strategy as in reference[9]but follow the notation of[10]that is slightly diﬀerent than [9].We seek a bosonic theory which reproduces correctly the low-energy regime of the massive fermionic theory.To begin with we deﬁne the G-current,j aµ=¯ψi t a ijγµψj,(51) whereψi are N two-component Dirac spinors in the fundamental representation of G,i,j=1,...,N and a= 1,...,dim G.Here t a and f abc are the generators and the structure constants of the symmetry group G,respectively and j aµis a G-current.The(Euclidean)fermionic partition function for the three-dimensional massive Thirring model is,Z T h= D¯ψDψe− ¯ψi(∂/+m)ψi−g22 d3x j aµj aµ= D aµe− d3x tr(12g2 d3x tr(aµaµ).(54)The determinant of the Dirac operator is an unbounded operator and requires regularization.For D=2this deter-minant can be computed exactly,both for abelian and non-abelian symmetries.Based on general grounds only,one may say that this determinant consists of a Chern-Simons action standing as the leading term plus an inﬁnite series of terms depending on the dual of the vectorﬁeld,˜Fµ∼ǫµνλ∂νAλ,including those terms that are non-local andnon-quadratic in˜Fµ.For the D=3the actual computation of this determinant will give parity breaking and parity conserving terms that are computed in powers of the inverse mass,χln det(i∂/+m+a/)=aµaνaλ),(56)3is the non-abelian Chern-Simons action and the parity conserving contributions,inﬁrst-order,is the Yang-Mills action1I P C[a]=−16πS CS[a](59) Using this result we can write Z T h in the formZ T h= D aµexp(−S SD[a]),(60) where S SD is the non-abelian version of the self-dual action introduced in[5],S SD[a]=116πS CS[a](61)Therefore,to leading order in1/m we have established the identiﬁcation Z T h≈Z SD.Now,recalling that the model with dynamics deﬁned by the non-abelian self-dual action is equivalent to the Yang-Mills-Chern-Simons theory,we use this connection to establish the equivalence of the non-abelian massive Thirring model and the YMCS theory asZ T h≈Z Y MCS.(62) It is interesting to observe that the Thirring coupling constant g2/N in the fermionic model is mapped into the inverse mass spin1massive excitation,m=π/g2.Now comes an important observation.Unlike the master approach,our result is valid for all values of the coupling constant.The proof,based on the use of an“interpolating Action”S I,is seen to run into trouble in the non-abelian case.That the non-abelian extension of this kind of equivalences is more involved was already recognized in[7]and [10],and shown that the non-abelian self-dual action is not equivalent to a Yang-Mills-Chern-Simons theory(the natural extension of the abelian MCS theory)but to a model where the Yang-Mills term vanishes in the limit g2→0 [10].B.Current IdentitiesTo infer the bosonization identities for the currents which derive from the equivalence found in the last section,we add a source for the Thirring current leading to the following functional generator,Z T h[b]= D¯ψDψD aµe− d3x ¯ψ(i∂/+m+a/+b/)ψ+1tr d3x bµbµ· D aµe−S SD[a]+12g2after shifting aµ→aµ−bµ.In order to connect this with the Yang-Mills-Chern-Simons system we repeat the steps of the last section to obtain,Z T h[bµ]≈Z MCS[bµ](64) We have therefore established,to order1/m,the connection between the Thirring and self-dual models in the non-abelian context,now in the presence of sources.This is,in its most general form,the result we were after.It provides a complete low-energy bosonization prescription,valid for any g2,of the matrix elements of the fermionic current.From(64)we see,from simple diﬀerentiation w.r.t.the source,that the bosonization rule for the fermion current,to leading order in1/m,readsj aµ→iχπ)ǫµν∂νφwhile in this case it should be considered as the analog of the Wess-Zumino-Witten currents.Notice that as in the abelian case the bosonized expression for the fermion current is topologically conserved.We thus see that the non-abelian bosonization of free,G-charged massive fermions in2+1dimensions leads to the non-abelian Chern-Simons theory,with the fermionic current being mapped to the dual of the gaugeﬁeld strength. This result holds only for length scales large compared with the Compton wavelength of the fermion,since our results were obtained for large fermion mass.It is important to notice that the limit g2→0used in earlier approaches corresponding to free fermions(but not to an abelian gauge theory)was not taken here at any stage.This is important since Yang-Mills coupling is proportional to g2,which is why we are left with a Yang-Mills-Chern-Simons action and not the pure Chern-Simons theory of[10].V.CONCLUSIONSThe rationale of diﬀerent phenomena in planar physics have greatly beneﬁtted from the use of2+1dimensionalﬁeld theories including the parity breaking Chern-Simons term.In this scenario it is important to establish connections among diﬀerent models so that a unifying picture emerges.In this context we have shown,in earlier work,that the soldering formalism has established a direct link between self-dual models of opposite helicities with the Proca model [14].Other instances includes the recent extension of the functional bosonization program interpolating from fermions to bosons in a coherent picture[9,10].In the context of theﬁrst it has been argued that the soldering formalism is equivalent to canonical transformation albeit in the Lagrangian side while for the later the mentioned mapping between SD and MCS models has been used to establish a formal equivalence between the partition functions of the abelian version of MTM and a theory of interacting bosons.The non-abelian extension of this analysis,for the full range of the coupling constant,has been the main concern of the present work since only partial results were reported in the literature.Other directions have also been investigated,with new results,that includes the proof of the self-duality property of(18)and the coupling with G-charged dynamical matterﬁelds.Our analysis has shown how the gauge lifting approach sheds light on the question of dual equivalence between SD and topologically massive theories with new results for the non-abelian case.This discussion becomes the central issue when deriving bosonization rules in D=3,for fermions carrying non-abelian charges since,up to date,only prescriptions based on the Master action of Ref.[7]were used,apart from[12]with conclusions consistent with[10]. These derivations of the bosonization mappings suﬀered from well known diﬃculties related to the dual equivalence, restricting the results to be limited to weak coupling constant only.Therefore,regarding the non-abelian bosonization in D=3dimensions,we believe that the method developed here,which is simpler and better suited to deal with non-abelian symmetries,completes the program initiated in[10]and conﬁrms the exact identities found in[22,23].This new approach has also been used with dynamical fermionicﬁelds leading naturally to the necessity of a Thirring like term to establish the equivalence of the fermionic sectors in both sides.Such equivalence may be extended to the scalar case[21].The bosonization for D≥4poses no diﬃculties as long as the fermionic determinant can be evaluated in some approximation and is expected to yield a gauge invariant piece.This is of importance since the description of chargedfermionicﬁelds in terms of gaugeﬁelds has brought new perspectives and a deeper insight on the non perturbative dynamics of planar physics[30]that might be extended to higher dimensions.。

德国专家阿明温格勒讲话

德国专家阿明·温格勒讲话产品质量只有通过受过培训的人才能得到，而受过培训的人也只有通过职业培训的人才能得到，其中一种培养人才的体系就是“双元制”体系。

“双元制”体系在德国应该说取得了很大成就，他想说到“双元制”这个概念可能在座的很多领导会想，我们的很多学校现在进行“双元制”培训，他也知道很多学校在开展“双元制”但是他只是觉得是个开始。

“双元制”的内容并不仅仅是需要学生一方面在学校培训，一方面去企业，做到这一点还远远不够，那他在做报告之前他先讲一条吧，如果在他今天下午的报告中有些观点比较尖锐，或者不是很中听的话，他请大家原谅，他虽然在中国生活很长时间，但中国人比较委婉的说话方式，他还是学不会，那他现在就开始他的这个报告，他先给大家介绍一下，在德国学校的教育。

·德国学校教育在德国小学一共是四年。

当学生完成四年小学教育的时候呢？他要决定上（德国一共有三种中学）三种中学中的哪种呢？有一种中学是人文中学，上完后一旦有毕业证可直接上大学；另外一种叫实验中学只上四年，还有一种主体中学只上三年。

总的来说有三种不同中学，那么这个学生上完四年中学后他要决定上哪一种学校，当然在德国这个社会的主流意识也是想让孩子上人文中学，之后去上大学。

那也就是说上完四年小学然后再去上三年的主体中学，再去上三年职业学校。

这种路呢他要小心地表达，也许他是留给那些学习成绩不是特别好的学生。

但现在企业对他自己的员工的素质要求。

不是越来越低反而是越来越高。

本来呢应该是主体中学毕业的学生，他应该去做专业工人的，本来是这样一条路。

但现在由于企业的要求不断增加，而主体中学毕业的学生，他相比之下他的基础稍微要差一些，所以现在德国也面临一种困难，也京是说主体中学毕业的学生他通常没办法达到企业对人才的素质要求。

现在的情况是这样子，很多企业本来应从主体学校招收学徒的学生，但现在他反而从实践中学成人文中学招收这个学生。

就今天上午的发言中人们也提到在中国以后也要进行十二年的义务教育。

人工语法范式的经典实验

人工语法范式的经典实验摘要：一、引言二、人工语法范式的起源和发展1.乔姆斯基的生成语法理论2.人工语法范式的实验研究三、经典实验介绍1.斯皮尔曼的实验2.麦克雷的实验3.费尔默的实验四、实验结果和讨论1.对乔姆斯基理论的验证2.对人类语言习得过程的启示五、人工语法范式的应用和挑战1.在语言教学中的应用2.面临的理论和实践挑战六、结论正文：一、引言人工语法范式，作为语言学领域的一种重要研究方法，起源于20世纪50年代乔姆斯基的生成语法理论。

通过设计特定的语法规则和实验环境，研究者们试图探讨人类语言习得的过程和机制。

本文将对人工语法范式的经典实验进行介绍和分析。

二、人工语法范式的起源和发展20世纪50年代，美国语言学家乔姆斯基提出了生成语法理论，认为人类具有内在的语言能力，可以通过一套普遍的语法规则生成无数合法的句子。

这一理论为人工语法范式的实验研究奠定了基础。

在乔姆斯基理论的指导下，许多研究者开始设计各种人工语法实验，以探讨语法规则的习得过程。

这些实验通常包括两个部分：语法规则和任务。

实验参与者需要根据给定的语法规则，完成特定的任务，如生成句子或判断句子的正确性。

三、经典实验介绍（1）斯皮尔曼的实验斯皮尔曼在1960年代进行了一系列经典的人工语法实验。

他设计了一个简单的语法规则，要求参与者根据规则生成句子。

实验结果表明，参与者在掌握了语法规则后，能够有效地生成符合规则的句子。

这一实验验证了乔姆斯基的理论，也为人工语法范式的发展提供了支持。

（2）麦克雷的实验麦克雷在1970年代对人工语法范式进行了进一步的拓展。

他设计了一个更为复杂的语法规则，并引入了否定词。

实验结果显示，参与者在学习了语法规则后，能够正确地生成和理解包含否定词的句子。

这一实验进一步证实了乔姆斯基理论的正确性。

（3）费尔默的实验费尔默在1990年代对人工语法范式进行了更为深入的研究。

他设计了一个更为复杂的语法系统，并引入了词汇和语义因素。

拉斐尔·费尔默：德国的5R青年

拉斐尔·费尔默：德国的5R青年作者：暂无来源：《环球慈善》 2013年第9期文／陈美薏图/CFP费尔默贯彻无钱的生活方式：他们一家的衣服来自慈善机构的赠予；住在教会的活动中心，以整理花园，修缮房屋及协办公益活动抵房租、电话费和上网费；脚踏车是他的代步工具，长途则靠拼车或搭便车。

一定要追求经济成长，人类文明才能进步？一定要有钱，日子才过得下去？德国青年拉斐尔·费尔默不愿相信，他拒绝让金钱主宰生命，虽身无分文，却过着富足的日子，食、衣、住、行，样样不缺。

他要以个人经验唤醒世人，假如地球的资源能以“全球化的观点”公平地共享，如果金钱的重要性不被扭曲，汲汲营营或强取豪夺都变得多余，美债欧债怪兽都不会出现，人可以活得更幸福，地球可以更和谐。

费尔默把他的社会运动取名为Forwardthe(R)evolution，意思是以和平、永续的方式，加速革命，推动人类的进化，塑造一个公平、健康的社会，与地球和谐共生。

关键字全是re开头的，包括拒绝浪费(refuse)、修理代替丢弃(repair)、减少垃圾(reduce)、资源回收(recycle)、资源再利用(reuse)等。

拒绝金钱主宰生活150年前就实现工业化的德国属于标准的富裕社会，根据联合国的统计，德国约四成的食物是被丢弃的。

其中有部分是过期的，而部分被迫下架，只因卖相不好、不够生鲜诱人。

许多过期的食物其实也不是真的坏掉，只是厂商加速代谢的障眼法。

费尔默强调，他厌恶富裕社会的假性需求及浪费，因此决意抵制金钱。

在德国，即使到别人家院子里捡垃圾也属盗窃行为，是犯法的。

所以，刚开始的时候，费尔默得趁夜黑风高，到超市后院的垃圾桶展开抢救行动。

“翻垃圾桶不恶心，朱门酒肉臭才恶心，以邻为壑才丢脸。

”费尔默写信给柏林各连锁超市，宣导其“食物分享”的理念。

后来，拥有30家分店的有机超市BioCompany首先响应，同意费尔默每星期两次前去清理废品。

回收的食物多得吃不完，过剩的全被放到一个名为“食物分享”的网络上，供人自由取用。

ChernSimons

k
1
k
8FEOFTEBZ "VHVTU
SUSY YMCS Theory on Torus (Witten)
★ Index Calculation on Two Torus of Size L ★ Small Torus Limit and all KK Modes are Ignored. ★ Low Energy Dynamics: Flat Diagonal Connections=constant
2+1 Dim Gravity (2)
★ Gauge Connection
★ Gauge Transformation =inﬁnitesimal diffeomorphism and Lorentz
transformation modulo Einstein equation.
★ Zero Field Strength
★ Gauge Transformation and Invariance
★ Gauss Law
★ Charge
★ Degrees of Freedom: In 4-dimension, two helicity
★
In 3-dim, one massless scalar
8FEOFTEBZ "VHVTU
★ Lagrangian ★ Momenta and Gauss Law ★ Hamiltonian ★ Quantization ★ The Wave Function ★ Decompose
8FEOFTEBZ "VHVTU
Quantization of Pure Chern-Simons
is identical to Einstein Eq..

德国著名化学家——埃米尔·费雪

德国著名化学家——埃米尔费雪
秋月
【期刊名称】《青苹果：高中版》
【年(卷),期】2006(000)0Z1
【总页数】2页(P94-95)
【作者】秋月
【作者单位】
【正文语种】中文
【中图分类】G634.8
【相关文献】
1.德国著名化学家——迈尔 [J], 刘春生;
2.最年轻的博士埃米尔·费雪 [J], 秋月;李幅厚（推荐）
3.《德国著名化学家莱奥波特·盖墨林及盖墨林手册》 [J], 刘晓宁
4.永恒的友谊——怀念德国著名历史学家费路教授 [J], 张宪文
5.一半是天使,一半是魔鬼——记德国著名物理化学家、化学战之父费茨·哈伯 [J], 邓玉良
因版权原因，仅展示原文概要，查看原文内容请购买。

那些年在诺贝尔奖出没的心理学家

2002年诺贝尔经济学奖授予了行为经济学和实验经济学的先驱者：美国普林斯顿大学的丹尼尔·卡尼曼（Daniel Kahneman）和美国乔治·梅森大学的弗农·史密斯（Vernon Smith）。
托马斯·特兰斯特勒默
托马斯· 特朗斯特罗姆，
瑞典著名诗人，同时是一位心理学家和翻译家，生于1931年。1954年发表诗集《17首诗》，轰动诗坛。至今共发表诗歌200余首。曾多次获诺贝尔文学奖提名，并终于在2011年10月6日获得诺贝尔文学奖
斯佩里
美国神经心理学家，用测验
的方法研究了裂脑病人的心理特征，证明大脑两半球的功能具有显著差异，提出两个脑的概念。曾荣获国家科学奖，1960年当选为国家科学院院土，1971年获美国心理学会颁发的杰出科学贡献奖，1981年获诺贝尔生理学奖。
丹尼尔·卡尼曼
丹尼尔· 卡尼曼1934年生于以色列，具有以色列与美国双重国籍，1961年获得加州大学伯克博士学位。之后相继担任以色列希伯来大学、加拿大不列颠哥伦比亚大学、美国加州大学伯克教授。自1993年起，普林斯顿大学心理学和公众事务学教授。
不愿作心理学家的心理学家——巴甫洛夫
1904年的第4届诺贝尔奖颁奖
俄国科学家巴甫洛夫就获得了诺贝尔生理或医学奖。不把他当作第一个获得诺贝尔奖的心理学家，原因有二，一是巴翁从来都不承认自己是心理学家；二是他获奖并非由于其尽人皆知的关于经典条件反射的研究，而是因为其在消化生理学研究中的巨大贡献而获此殊荣。
那些年在诺贝尔奖出没的心理学家
诺贝尔奖
诺贝尔奖是以瑞典著名化学家、工业家、
硝化甘油炸药发明人诺贝尔的部分遗产作为基金创立的。
诺贝尔奖
从1901年第一届诺贝尔奖开始颁发到现在

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a r X i v :h e p -t h /0204059v 2 25 J u l 2002Chern-Simons Term for BF Theory and Gravity as a GeneralizedTopological Field Theory in Four DimensionsHan-Ying Guo 1,2,∗Yi Ling 2,3,†Roh-Suan Tung 2,4,‡and Yuan-Zhong Zhang 1,2§1CCAST (World Laboratory),P.O.Box 8730,Beijing 100080,China2Institute of Theoretical Physics,Chinese Academy of Sciences P.O.Box 2735,Beijing 100080,China3Center for Gravitational Physics and Geometry,Department of Physics,Pennsylvania State University,University Park,PA 16802,USA and 4Department of Physics,University of California,Davis,CA 95616,USA(Dated:February 1,2008)A direct relation between two types of topological ﬁeld theories,Chern-Simons theory and BF theory,is presented by using “Generalized Diﬀerential Calculus”,which extends an ordinary p −form to an ordered pair of p and (p +1)−form.We ﬁrst establish the generalized Chern-Weil homomormism for generalized curvature invariant polynomials in general even dimensional mani-folds,and then show that BF gauge theory can be obtained from the action which is the generalized second Chern class with gauge group G .Particularly when G is taken as SL (2,C )in four dimen-sions,general relativity with cosmological constant can be derived by constraining the topological BF theory.PACS numbers:04.60.Ds,04.20.GzI.INTRODUCTIONIn the last few years one of the most important progress in quantum gravity is that deep relations between gravity and the gauge ﬁelds have been further disclosed.In string theory one seminal work is the proposed AdS/CF T correspondence[1],which implies there might exist a gen-eral duality between gravity theory and Yang-Mills the-ory.On the side of loop quantum gravity,the replac-ing of geometrodynamics by connection dynamics has also shed light on the analogy of gravitational ﬁelds and gauge ﬁelds[2].In particular,there has been recently much interest in the relations between topological ﬁeld theory and gravity[3,4].Besides the well known fact that three dimensional gravity is simply a topological ﬁeld the-ory without local degrees of freedom[5],recent progress shows that even in higher dimensions Einstein’s general relativity and supergravity in Ashtekar formalism may also be written as topological ﬁeld theories with extra constraints[6,7,8,9,10][22].Since no pre-exiting met-ric or other geometric structure of spacetime is needed in the context of topological ﬁeld theory,the advantages of taking this framework as a starting point to explore the background-independent quantum theory of gravity have been revealed in the context of loop quantum grav-ity from many aspects.Two remarkable programmes are “state sum model”advocated by Crane and Yetter[3]and “spin foam model”by Rovelli and Reisenberger[11].In both programmes such connections between gravity and topological ﬁeld theories allow one to apply the elegant2 GR with cosmological constant in the absence of mattercan be derived by a constrained topologicalﬁeld theory(Section5)related to holographic formulation[9].II.CHERN-WEIL HOMOMORMISM INGENERALIZED DIFFERENTIAL CALCULUSLet us consider a principle bundle P(M,G)and intro-duce the generalized gaugeﬁelds in Generalized Diﬀer-ential Calculus on it.For the semisimple gauge groupG with Lie algebra g,a generalized g-valued connection1-formﬁeld A is deﬁned as a g-valued pairing of a1-formand a2-formA=(A p,B p)T p=(A,B),T p∈g,(1)where A is the ordinary g-valued connection1-form andB the g-valued2-form which is assumed as gauge covari-ant under the gauge transformations in order to introducea generalized gauge covariant curvature FF=d A+A∧A=(dA+A∧A+kB,dB+A∧B−B∧A)=(F+kB,DB).(2)It satisﬁes the generalized Bianchi identity:DF=d F+A∧F−F∧A=(DF,D2B)≡0.(3)In order to consider the topological invariants in theframework of this Generalized Diﬀerential Calculus,letusﬁrst brieﬂy remind the properties of the curvature in-variant symmetric polynomials on P(M,G).Taking a connection1-form A on the bundle,the cur-vature2-form is F=dA+A∧A.The curvature invari-ant symmetric polynomial,say,for simplicity,P(F m)isa2m-form on MP(F m)=P(F,···,Fm)(4)satisfying(a)P(F)is closed,i.e.,dP(F m)=0,(5)(b)P(F m)has topologically invariant ly,it satisﬁes the Chern-Weil homomormism formula:P(F m1)−P(F m0)=dQ(A0,A1),(6)whereQ(A0,A1)=1P(A1−A0,F m−1t)dt,(7)where A0and A1are two connection1-forms,F0and F1 the corresponding curvature2-forms,A t=A0+tη,η=A1−A0,(0≤t≤1),(8)the interpolation between A0and A1,F t=dA t+A t∧A t.(9) Since P(F m1)and P(F m0)diﬀer by an exact form,their integrals over manifolds without boundary give the same results and Q(A0,A1)is called the secondary topological class.For the generalized connection A and curvature F in Generalized Diﬀerential Calculus,it can be proved that the generalized curvature invariant symmetric polyno-mial,say,for simplicity,P(F m)also satisﬁes the similar closed condition and the generalized Chern-Weil homo-mormism formula:(i)d P(F m)=0,(10)(ii)P(F m1)−P(F m0)=d Q(A0,A1).(11) Let us now sketch the proof.For proving(i),it is a straightforward consequence by using the generalized Bianchi identity(3).To prove(ii),let us take two distinct generalized con-nections A0,A1and the corresponding curvatures F0, F1on the bundle.LetA t=A0+tη,η=A1−A0,(0≤t≤1),(12) and the corresponding curvature isF t=d A t+A t∧A t.(13) It is easy to see thatddtP(F mt)=m P(D tη,F m−1t)=m D t P(η,F m−1t)=m d P(η,F m−1t),(15) ThusP(F m1)−P(F m0)=d 10P(A1−A0,F m−1t)dt=d Q(A0,A1).(16)This shows that the generalized characteristic polynomi-als with respect to diﬀerent connections only diﬀer by an exact form in Generalized Diﬀerential ly, they are also homomormism.Q(A1,A0)is called the generalized Chern-Simons secondary class.Thus,we have established the generalized Chern-Weil homomormism for generalized curvature invariant poly-nomials in any even dimensional manifolds.But,their topological meaning should be as same as before.3III.GENERALIZED CHERN-SIMONS TERMFOR BF THEORYConsider an action on the base manifold of P(M4,G) of the form:S T= M4L T= M4T r(F∧F).(17)The Lagrangian4-form L T can be given by taking A1= A and A0=0in(11),thenT r(F∧F)=d Q CS,(18) Q CS is the generalized local Chern-Simons3-form,i.e., the pairing of a3-form and a4-formQ CS=T r(A∧F−13A∧A∧A+kA∧B),T r(A∧DB+B∧F+kB∧B)).(19) In the pairing,the3-form is the usual Chern-Simons term up to a kT r(A∧B)term.On the other hand,the generalized Lagrangian4-form in(17)is a pairing of a4-form and a5-form:L T=T r((F∧F+2kB∧F+k2B∧B),2(F∧DB+kB∧DB)).(20) Using the Bianchi identity,we can rearrange the5-form so thatL T=T r((F∧F+2kB∧F+k2B∧B),d(B∧F+kB∧B)).(21) Theﬁrst term is just the BF Lagrangian up to an F∧F term,the second term is a total derivative of the BF Lagrangian.Thus the pairing of the action(17)shows a relation be-tween two types of topologicalﬁeld theories,the Chern-Simons type and the BF type in four dimensions:S T[A]= M4L T= M4d Q CS= M4T r F∧F+2kB∧F+k2B∧B .(22)We can obtain theﬁeld equations by varying the La-grangian with respect to the generalized gauge potentials, i.e.,the g-valued generalized connection1-form.With these generalized gauge potentialsﬁxed at the boundary, theﬁeld equations areD(F+2kB)=0,(23)k(F+kB)=0.(24) The second equation gives F=−kB which can be sub-stituted into theﬁrst equation and leads to the Bianchi identity.Note that we start up with any2-form B in the generalized connection.Then with the action given by the generalized second Chern class,it gives B=−(1/k)F.Therefore,the action(17)does not give any dynamics.However,it should be noted that with k=−1all geometrical properties of the bundle P(M4,G)are re-derived from a generalized topologicalﬁeld theory of the BF type with a generalized Chern-Simons term associ-ated in Generalized Diﬀerential Calculus.IV.GENERALIZED CONNECTION WITHSL(2,C)GAUGE GROUP ONPSEUDO-RIEMANNIAN MANIFOLD M4Let us consider the tangent bundle T(M4)≃P(M4,SL(2,C))on the base manifold(M4,g)as the pseudo-Riemannian spacetime manifold with signature sign(g)=−2.The sl(2,C)algebraic relation reads[23]: [M AB,M CD]=ǫC(A M B)D+ǫD(A M B)C,(25)whereǫC(A M B)D=12(ǫAMǫBN+ǫANǫBM).(26)Since SL(2,C),the covering of the Lorentz group SO(3,1),is the gauge group of the bundle,we may in-troduce an sl(2,C)-valued generalized connection1-form in the framework of Generalized Diﬀerential CalculusA=(ωAB,B AB)M AB,(27) whereωAB is an ordinary sl(2,C)-valued connection1-form on the bundle and B AB is an SL(2,C)-gauge co-variant2-form.Given the connection A,the generalized curvature(F=F p T p=F AB M AB)is given byF AB=(R AB+kB AB,DB AB).(28) where R AB=dωAB+ωA C∧ωCB is the SL(2,C)cur-vature2-form.The generalized Bianchi identity is given byDF AB=(DR AB,D2B AB)≡0.(29) A simple generalized Lagrangian4-form in(17)using this connection A isS SL(2,C)[A]= M4L SL(2,C)= M4F AB∧F AB = M4R AB∧R AB+2kR AB∧B AB+k2B AB∧B AB.(30) Theﬁeld equations are obtained by varying the La-grangian with respect to the sl(2,C)-valued generalized4 connection1-form withﬁxed value at the boundary.Thisleads to theﬁeld equationsD(R AB+2kB AB)=0,(31)k(R AB+kB AB)=0.(32)The second equation gives R AB=−kB AB,which can besubstituted into theﬁrst and leads to the Bianchi iden-tity.Therefore,as expected,the action S SL(2,C)does notgive any dynamics.Moreover,when k=−1,all proper-ties in the pseudo-Riemannian geometry on(M4,g)arerecovered by the generalized topologicalﬁeld theories ofBF type in four dimensions.V.GRA VITY AS A GENERALIZEDTOPOLOGICAL FIELD THEORYLet us now consider pure gravity in four dimen-sions.As in the previous section,the spacetime manifold(M4,g)is pseudo-Riemannian with signature sign(g)=−2and the gauge group now is SL(2,C).Note that the4-form Bianchi identity(29),D2B AB=0,looks similar to the identity D2(e AA′∧e B A′)=0,where e AA′is the frame1-form.Thus we may introducean ansatz B AB=l−2e AA′∧e B A′,where l is a dimen-sional constant.The sl(2,C)-valued generalized connec-tion1-form(27)now becomes[24]A=(ωAB,1l2e AA′∧e B A′,1l2R AB∧e AA′∧e B A′+k2l2e AB′∧e B B′∧e B A′+c.c.=0,(37)which is the Einstein equation with a cosmological con-stantΛif we setΛbyΛ=kl2e AA′∧e B A′−B AB)+c.c.= M4R AB∧R AB+2kR AB∧B AB+k2B AB∧B AB+λAB∧(15In order to include the matter,there might be at least two possibilities.Theﬁrst may link with the Kaluza-Klein formalism,since the gauge theories can be formu-lated as Kaluza-Klein theories on Minkowski spacetime. Therefore,it might be possible to deal with gauge the-ories as generalized topologicalﬁeld theories in our ap-proach.Of course,there should be certain restriction to the dimensions of the gauge groups.Furthermore, this approach might be generalized to fermions and Higgs [16].On the other hand,to generalize it to supergravity might be another possibility.For instance,the General-ized Diﬀerential Calculus may be generalized to super-symmetric cases.Then,supergravity can be obtained by gauging the OSp(1,4)group with the generalized con-nection.It is interesting to see that the present formulation only works for4-dimensional BF theories with B a2-formﬁeld.On one hand,it is reasonable to establish the relation between the Donaldson-Witten invariants in four dimensions and the topologicalﬁeld theory such as the BF type.On the other hand,however,especially for the GR with cosmological constant,it seems amazing that the dimensions of our nature is also four.If this formula-tion could not be generalized to arbitrary higher dimen-sions,whether this dimension four has more profound meaning rather than just a coincidence.This question has to be left for further study and inspiration.Appendix:Generalized Diﬀerential CalculusA generalized p-form[14][15],p a,is deﬁned to be an ordered pair of an ordinary p-form pαand an ordinary (p+1)-form p+1αon an n-dimensional manifold M,that ispa≡(pα,p+1α)∈Λp×Λp+1,(39)where−1≤p≤n.The minus one-form is deﬁned to be an ordered pair−1a≡(0,0α),(40)where0αis a function on M.The product and derivatives are deﬁned bypa∧qb≡(pα∧qβ,pα∧q+1β+(−1)q p+1α∧qβ),(41)d p a≡(d pα+(−1)p+1k p+1α,d p+1α),(42) where k is a constant.These exterior products and derivatives of generalized forms satisfy the standard rules of exterior algebrapa∧qb=(−1)pqqb∧p a,(43) d(p a∧qb)=d p a∧qb+(−1)p p a∧dqb,(44) and d2=0.For a generalized p-form p a=(pα,p+1α),the integration on M p can be deﬁned as usual byM ppa= M p(pα,p+1α)= M p pα.(45)AcknowledgmentsWe would like to thank Professors Y.F.Liu,Q.K. Lu,K.Wu,Z.Xu and M.Yu for valuable discussions. RST thanks Prof S.Carlip for helpful discussions.This project is in part supported by NNSFC under Grants Nos.90103004,10175070,10047004,19835040and also by NKBRSF G1*******.[1]O.Aharony,S.S.Gubser,J.Maldacena,H.Ooguri andY.Oz,“Large Nﬁeld theories,string theory and gravity”, Physics Reports323,(2000)183;hep-th/9905111. 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