Geometry & Topology in Physics

Jan Martin Pawlowski, winter term 2008/2009

Script

	Introduction
	1 Symmetries & topological exitations
	1.1 Complex scalar field in d dimensions
	1.2 Solitons
	1.3 Fermions in a solitonic background
	1.4 Dilute gas expansion
	2 Gauge theories & homotopy
	2.1 Abelian Higgs model
	2.2 Homotopy: fundamental group
	2.3 Higher homotopy groups
	3 Non-Abelian gauge theories
	3.1 Basics
	3.2 Instantons in SU(2)
	3.3 Fermionic zero modes & Atiyah-Singer index theorem
	3.4 Gauge Anomalies
	3.5 Monopoles & dyons
	4 Seiberg-Witten theory*
	4.1 Supersymmetry
	4.2 N=2 Susy Yang-Mills theory
	4.3 Low energy effective action