Course Identification

QM I, II

1) Introduction. Conventions. Perturbation theory and Feynman diagrams from Path Integrals (scalars and fermions). Computation of tree-level diagrams. The S-matrix.

2) Computation of one-loop diagrams, regularization and renormalization (perturbative). Dimensional regularization. Renormalizable field theories. The optical theorem and the LSZ reduction formula.

3) Scale-dependence of coupling constants and beta functions, the renormalization group, the Wilsonian effective action, marginal and relevant operators, fixed points.

4) QED – quantization of gauge fields, gauge fixing and the Faddeev-Popov procedure, Feynman diagrams, Ward identities. Computations at tree-level and at one-loop, renormalization.

5) An introduction to non-Abelian gauge theories. Qualitative discussion of non-perturbative features of QCD.

6) (Time permitting) Symmetries in QFT, Goldstone’s theorem, the Higgs mechanism.

Upon successful completion of this course students should be able to:

1. Perform perturbative computations, both at tree-level and at higher orders (loops), in any quantum field theory, including scalars, fermions, and gauge fields. This includes regularizing and renormalizing the theory if necessary, and computing the beta functions indicating how coupling constants vary with the scale. Students should be able to perform both computations of correlation functions, and of the S-matrix.
2. Relate quantitative QFT calculations to high-energy particle physical phenomena, e.g. scattering cross sections or particle decay processes.
3. Take more advanced courses, including QFT2 and advanced courses like supersymmetry, and other related topics.