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⇒ WS 11/12: Geometry & Topology in Physics
Geometry & Topology in Physics
Lecture
Thomas Gasenzer and Jan Martin PawlowskiTuesday, 11:1513:00, SR Pw 19 [LSF]
Wednesday, 09:1511:00, 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 IIV, 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
 NonAbelian gauge theories:
Setting, instantons, zero modes, collective coordinates & moduli space, fermionic zero modes & AtiyahSinger index theorem, topology & confinement
 Gauge anomalies:
Cocycles, WessZumino consistency condition, consistent & covariant anomalies
 Topology & dynamics:
Dynamics, vortices, scaling
 SeibergWitten:
Supersymmetry, chiral multiplets, N=2 Susy YangMills, superconformal WardId'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  NorthHolland  
WuKi Tung  Group Theory in Physics  World Scientific  
ZinnJustin  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 