Math 712 — Topics in Analysis

Spring 2003

Instructor: Leonard Gross

Time: MF 2:35-3:50

Room: MT 205

Tentative course outline:

Starting from scratch in physics, we will take a path aimed at getting to the currently most widely accepted theory of elementary particles and their interactions, the "Standard model''.

Many physics courses spend a good deal of course time teaching the mathematics necessary to understand the physics. The general aim of this seminar will be to "review'' some parts of physics, making use of the mathematics background that most second year graduate students already have.

Here is an optimistic outline: the topic in physics is followed by the topic in mathematics that is closest.

  1. Newtonian mechanics.
   (Flows on manifolds.)
  1. Electricity and magnetism.
   (Group representations.)
  1. Quantum mechanics.
   (Unbounded operators.)
  1. Yang-Mills fields.
   (Connections on vector bundles and principle bundles.)
  1. Quantum field theory.
   (Tensor algebras and holomorphic functions in infinitely many variables.)
  1. Bosons.
  2. Fermion.
   (Exterior and Clifford algebras.)

The topics in the second column will be the topics actually lectured on by you and me. The relation to the topics in the first column will be largely lectured on by me.

Needed background:

Mathematics: 631, 611, 652. 713 would help. Some Riemannian geometry would help.

Physics: High school physics.