Mitarbeiter

Geometry & Topology in Physics

Lecture

Wednesday, 09:15-11:00, every 2nd week, SR Pw 19
Practice group: tba.

Prerequisites - Content - Literature - Exercises & Bonus material - Script - Script WS 08/09 (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
		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