# SS16 Advanced Quantum Field Theory

## Syllabus

• Spontaneous symmetry breaking (non-linear sigma model)
• Effective theories at 1 loop
• Solitons in 2D (kink), 3D (vortices), 4D (monopoles)
• The U(1) problem and the strong CP problem
• Anomalies
• Instantons and Anomalies

## Lectures

Monday 10-12  (theory library, PH3343)
Thursday 10-12 (theory library, PH3343)

## Exercises

Friday 10-12  (Hilbert Raum, PH1141

## Prerequisites:

QFT1 (at TUM)

If your QFT course didn't cover path integrals, functional formalism or non-Abelian gauge theories, I suggest to read Anthony Zee's "Quantum Field Theory in a Nutshell" for a gentle introduction.

## Literature:

S. Weinberg - Quantum Field Theory (1 & 2)
Rajamaran - Solitons and Instantons
Shifmann - Advanced Topics in Quantum Field Theory
Coleman - Aspects of Symmetry
Preskill - Lecture notes (on his Caltech website)
Schwartz - Quantum Field Theory and the Standard Model

## Lecture Notes

12 Mathematical interlude: Introduction to homotopy theory and homotopy groups (2.6.2016)
13 Homotopy groups and vacuum manifolds (6.6.2016)

## Exercise Sheets

Exercise coordination: Reuven Balkin (T75)

Exercise 1 (sol1.pdf): O(N) model, and P&S 11.2 (pdf of P&S problem(to be discussed 22.4.)
Exercise 2 (sol2.pdf): Effective potential, Gross-Neveu Model P&S 11.3 (pdf of P&S problem(29.4.2016)
Exercise 3 (sol3.pdf): Anomalies (Fermion number non-conservation, SM anomalies) (13.5.2016)
Exercise 4 (sol4.pdf): Solitons (sine-Gordon, stability, winding number) (27.5.16)
Exercise 5 (sol5.pdf): Nielsen-Oelesen Vortex, BPS states (3.6.16)
Exercise 6 (sol6.pdf): Homotopy theory (17.6.16)
Exercise 7 (sol7.pdf): 5D fermions stuck to a brane, chiral localization (25.6.16)
Exercise 8 (sol8.pdf): Instantons (8.7.16)