Peskin量子场论习题解答(第三学期)

Physics 332–Problem Set #2(due Wednesday,April 26)1.Peskin and Schroeder,Problem 11.1.2.Peskin and Schroeder,Problem 11.2.3.Peskin and Schroeder,Problem 11.3.1

Physics 332–Problem Set #3(due Wednesday,May 3)1.Peskin and Schroeder,Problem 12.1.2.Peskin and Schroeder,Problem 12.2.You should show that,

with this βfunction,the mass m ψof the ψfield satisfies the Callan-Symanzik equation M ∂∂M +∂g m 12(4π)4+(4π)4+

Physics 332–Problem Set #4(due Wednesday,May 10)1.Peskin and Schroeder,Problem 12.3.2.Peskin and Schroeder,Problem 13.1.1

Physics 332–Problem Set #5(due Wednesday,May 17)1.Consider scalar electrodynamics:L =−14(F 6(φ48π224π2(5λ6λ(ϕ 2.Apply the methods of this problem to the Glashow-Salam-Weinberg model of weak interactions.(a)Compute the effective potential for the Higgs field to 1-loop order,ignoring all effects of quark masses but including the contributions of gauge fields.(b)Show that the theory has a first-order phase transition as a function of the renor-malized Higgs mass parameter μ2.(c)Show that this result implies a lower bound on the physical mass of the Higgs boson (the ‘Linde-Weinberg bound’).Compute the bound to leading order in coupling constants.(d)Now add in the contribution of the top quark.Show that,when the top quark mass is sufficiently heavy,the symmetry-breaking effect found in part (b)goes away.However,another pathology develops,in which,when m t is sufficiently large,the effective potential becomes negative at very large field values and causes an instability of the model.Estimate the value of the top quark mass,as a function of the Higgs boson and W boson masses,at which this instability takes place.2

Physics 332–Problem Set #6(due Wednesday,May 24)1.Peskin and Schroeder,Problem 17.1.2.In class,I sketched the derivation of the βfunction of a non-Abelian

gauge theory from the renormalization counterterms δ1,δ2,and δ3.Work through this calculation in full e the Feynman-‘t Hooft gauge.3.Peskin and Schroeder,Problem 16.3.Please note:This is a long calculation.The solution set for this problem set is 50pages long,of which 35pages are devoted to this problem.I do assure you that you will learn a considerable amount about how to calculation in gauge theories by doing this problem to the end.(Of course,it might be true that these are things that you never wanted to know ...)1