SS16 Advanced Quantum Field Theory




  • 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



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


Friday 10-12  (Hilbert Raum, PH1141


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.  


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

(Please log in with your TUM account.)

1 Introduction, spontaneous symmetry breaking (QM vs. QFT), discrete symmetries 
2 Continuous symmetries, non-linear sigma model, Coleman-Mermin-Wagner Theorem
3 SO(3) and partial symmetry breaking, general theorem, functional methods (effective potential, integrating out d.o.f.s).
4 Effective potential at 1loop, functional determinants, radiative symmetry breaking, anomalous scale invariance
5 Fermion functional determinant, Higgs mechanism (abelian, non-abelian), Superconductivity, (25.4.2016)

6 Anomalies 1: Feynman diagram calculation (axial vs. vector current conservation, linearly divergent integrals) (28.4.2016)
7 Anomalies 2: Path integral derivation (Fujikawa method)
8 Anomalies 3: Consistent chiral gauge theories (real rep's), anomaly cancellation in SM, scale Anomaly and beta function (9.5.2016)

 Introduction to Solitons and Instantons (19.5.2016)
10 Lyapunov stability, Derrick's theorem, Yang-Mills solitons (23.5.2016)
11 Nielsen–Olesen vortex, winding number, approximate solution, superconductor (30.5.16)

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

14 Magnetic monopoles, dyons, elementary features, topological current, 't Hooft-Polyakov
15 Soliton quantization, bound states and collective coordinates (13.6.16)

16 Tunneling: QM and the path integral, introduction to dilute instanton gas (16.6.16)
17 Instantons, collective coordinates and the periodic potential  (20.6.16)
18 Instantons in gauge theories part 1  (23.6.16)
19 BPS solution, collective coordinates and zero-modes, 1-loop corrections (27.6.16)
20 Instantons and fermion zero modes, theta angle and phase of fermion mass determinant, 't Hooft symbols (30.6.16)
21 Spectral flow and the non-perturbative creation of fermions, the eta-prime puzzle, U(1)-baryon violation (4.7.16)

22 Strong CP problem, motivation, Nelson-Barr solution, simple Axion models (KSVZ) (7.7.16)
23 Chiral Lagrangian, Gellmann-Oakes-Renner, QCD Axion mass, Axion Phenomenology (11. and 14.7.16) 


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)