Course Identification

• Quantum Mechanics 1
• Quantum Mechanics 2

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) (Time permitting) Fun with perturbation theory : Large N field theories and string theory.

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

5) 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.

6) An introduction to non-Abelian gauge theories.

7) Non-perturbative field theory – QCD (qualitative). 3d QED, instantons and confinement.

8) (Time permitting) Symmetries in QFT, Goldstone’s theorem, renormalization and symmetry, the Higgs mechanism (classical and quantum).

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. Demonstrate understanding of the possible phases of quantum field theories, and various methods to analyze and to identify which phase a specific theory is in. Understand the renormalization group and flows between different quantum field theories.
3. Take more advanced courses, including QFT2 and advanced courses in supersymmetry, string theory and other related topics.

The main book that will be used in the first part of the course M. Peskin and J. Schroeder, "An introduction to quantum field theory", but there are many other good books on this topic, and it is recommended to look at several different books. A more complete reading list will be given at the beginning of the semester.