Geometry & Topology in Physics


Thomas Gasenzer and Jan Martin Pawlowski

Tuesday, 11:15-13:00, SR Pw 19 [LSF]

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


      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