Math 993 Fall 2013

Topics in Gauge Theory

3 -- 3:50, Mondays and Wednesdays in Room C-517, Fridays in Room C-304 Wells Hall

Math Tools Professor Thomas H Parker
A-346 Wells Hall 353-8493
parker@math.msu.edu

Office hours:
Tuesday: 1-2
Wednesday 11-12
Thursday 11-12
and by appointment (email to set up time).


Goals: This course covers mathematical gauge theory. In content and organization, it will adapt the perspective of physicists. The aim is to integrate the physics viewpoint and intuition into the mathematical theory. The terminology of physics permeates the subject, but if often not understood by mathematicians. In particular, we will discuss quantum gauge theories.     

Prerequisites: Familiarity with manifolds and vector bundles. It will be very useful, but not strictly necessary, to have some knowledge of PDEs and Riemannian geometry.

Handouts:   Course Outline

Homework:     HW Set 1     HW Set 2     HW Set 3    HW Set 4    HW Set 5


Preliminary list of topics:

  1. Classical fields and Maxwell's equations as a gauge theory
  2. Spinors and the Dirac equation
  3. The Seiberg-Witten equations
  4. Second quantization
  5. Yang-Mills and general gauge theories
  6. Examples

Helpful reference books:

Other reference articles: