Geometry & Topology in Physics
Tuesday, 11:15-13:00, Pw 19 / SR [LSF]
Wednesday (lecture/Tutorial), 9:15-11:00,
Pw 19 / SR [LSF]
Wednesday, 1st of February 9:00-11:00
- Content
- Literature
- Exercises & bonus material
- Script
- Script winter term 2008/2009 (different focus)
Prerequisites: Theoretical Physics I-IV, basic knowledge of QFT
Content of lecture series
The lecture course provides an introduction to geometrical and
topological effects in physics, applications range from quantum
mechanics to quantum field theory.
- Outline in key words
-
Symmetries & topological exitations:
Scalar field theory, solitons, fermions & index theorems, dilute gas expansion, applications
- Gauge theories & homotopy:
Abelian Higgs model, Bogomol'nyi bound, homotopy, topological invariants & classification
- Non-Abelian gauge theories:
Setting, instantons, zero modes, collective coordinates & moduli space, fermionic zero modes & Atiyah-Singer index theorem, topology & confinement
- Gauge anomalies:
Cocycles, Wess-Zumino consistency condition, consistent & covariant anomalies
- Topology & dynamics:
Dynamics, vortices, scaling
- Seiberg-Witten:
Supersymmetry, chiral multiplets, N=2 Susy Yang-Mills, super-conformal Ward-Id's, dualities
Literature
| Coleman | Aspects of Symmetry | Cambridge University Press | |
| Göckeler & Schücker | Differential Geometry, gauge theories, and gravity | Cambridge University Press | |
| Nakahara | Geometry, Topology and Physics | Hilger | |
| Nash & Sen | Topology and Geometry For Physicists | Academic | |
| Rajaraman | Solitons and Instantons | North-Holland | |
| Wu-Ki Tung | Group Theory in Physics | World Scientific | |
| Zinn-Justin | Quantum Field Theory and Critical Phenomena | Oxford | |
| Schäfer, Shuryak | Instantons in QCD | Rev.Mod.Phys.70:323-426,1998 | |
| Lecture notes | |||
| Bruckmann | Topological objects in QCD | Lecture notes, Schladming winter school 2007 | |
| Lenz | Topological concepts in gauge theories | Lecture notes | |
| 't Hooft, Bruckmann | Monopoles, Instantons and Confinement | Lecture notes, Saalburg summer school 1999 |