Notes for Physics 752 (Prof. Agashe) – Spring 2022


The following are notes from online lectures based on topic:


(0). Outline of/Introduction to course


(I). QFT topics:


(A). Renormalization:


     (i). outline of program (in general)


     (ii). Degree of divergence (in general)


     (iii). List divergent amplitudes in QED


     (iv). Ward-Takahashi identity in QED


     (v). Regularization and adding counter-terms in QED for

           vacuum polarization (general discussion and calculation in DIMREG);

           vertex function and fermion self-energy


     (vi). Putting it all together (renormalization) for QED


     (vii). Running of QED coupling


     (viii) Summary of renormalizability of QED


     (B). Renormalizable theory for massive gauge bosons:
           (i). Motivation for studying/Introduction to Spontaneous Symmetry   
                Breaking (SSB)/Higgs mechanism 
           (ii). SSB for global case: discrete symmetry; basic idea of continuous 
           (iii). Global SSB: Nambu-Goldstone boson
           (iv). SSB for gauge theory (Higgs mechanism): basic idea in unitarity 
                  gauge (Nambu-Goldstone boson “eaten” by gauge boson, which   
                  then becomes massive)
           (v). Higgs mechanism:  renormalizable gauges (unitarity gauge as limit)
            (vi). Summary of Higgs mechanism
     (C).  Non-abelian (gauge) Theories (applicable to QCD and electro-weak)


         (i). Global non-abelian: basics (including motivation for this QFT topic);

              group theory; SSB


   (ii). Non-abelian gauge theories: (a). classical (including SSB) and (b).  



(II). Theory and Phenomenology of SM


(i). Overview of SM theory


(ii). Theory of EW sector of SM: (a). overview; (b). bosonic  and (c) fermionic sectors


(iii). EW sector phenomenology: no generational mixing (“non”-flavor): (a). overview; (b) details (separately, complete calculation of Z decay width)


(iv). Flavor phenomenology: (a). overview and (b). observables


(v). QCD: (a). history and (b). theory/phenomenology overview


(vi). QCD phenomenology (details of processes): (a). e+e- à all hadrons; (b). Deep Inelastic Scattering (separately, convenient form, specific to QED)

and (c). Hard scattering part of Hadron-hadron collisions (separately, convenient form, specific to Drell-Yan process)


(III). Beyond SM:


(a). overview of selected topics and


(b). (some) details of grand unified theories (GUT).



Extra/supplementary material:


    (1). Choice of Z1   getting rid of divergence in vertex function even for    

          fermions being off-shell (and photon momentum being non  



     (2). Proof (using Ward-Takahashi identity) of Z1 = Z2


     (3).  From Weinberg’s textbook on QFT: consideration as a candidate ground   

            state of a 50-50 superposition of the 2 “usual suspects” for ground states

            (for the case of real scalar mass^2 < 0, i.e., discrete symmetry), i.e.,    

            with positive/negative VEV for scalar field. 


(4). Comments on Pion-Nucleon system