Quantum field theory III

1) Brief foray into "axiomatic" QFT

-Unitary representations of the Poincaré group

- Fields, relativistic wave equations

- Cluster property and LSZ formula for the S-matrix

2) Path Integral approach to QFT

- Functional methods,  Effective action

- Equations of motion, Ward identities, Goldstone theorem

3)  Renormalization

- loop corrections and regularization methods

- renormalization with examples of its systematics

- applications to QFTs with scalars, fermions and Abelian gauge fields, in particular to Quantum Electrodynamics

4) The renormalization group

- asymptotic freedom and fixed points

- Callan-Symanzik equation

- renormalization of composite operators

5) Quantization of non-abelian gauge theories

- path Integral in gauge theories and Faddeev-Popov method

- ghosts and BRST symmetry

- physical states and unitarity

- Slavnov-Taylor identities and basics of renormalization

6) Form factors, scattering amplitudes, and the LSZ reduction formula

7) Infrared divergences (time permitting)

- soft photons and soft gravitons

- Lorentz invariance and current conservation (Weinberg)

- real and virtual emission of soft photons, cancellation of IR divergences

Throughout the course, emphasis will be placed on the logical relations between these concepts and on the assumptions entering their definitions.

Students enrolled through EPFL will complete additional take-home readings and exercises.