Math 542A/543A: Quantum Fields and Strings
Gerald Folland

Winter/Spring 2001, Monday/Wednesday/Friday 2:30-3:20

This course will be based on some subset of the material in the 2-volume set Quantum Fields and Strings: A Course for Mathematicians (AMS, 1999) that came out of a special year on that subject at the Institute for Advanced Study; material from other sources may also be incorporated.  The aim of the course, like that of the book, is not to provide a complete, rigorous development of anything, but rather to convey an understanding, in terms congenial to mathematicians, of some fundamental ideas of quantum physics leading up to the current research in string theory: quantum fields, functional integrals, renormalization, etc.

This is an impossibly ambitious goal for a 2-quarter course, and I will have to stake out a reasonable amount of ground to cover.  At present (8/26/00) I have not yet worked on this seriously, but can offer a few hints.  I intend to start with a review of the basics of classical quantum mechanics, and will try to make contact with concrete physical problems from time to time rather than dealing always with theoretical generalities. As a matter of personal taste, I will probably emphasize the analytical aspects over the geometric ones.  In any case, the audience should be warned that I expect to be learning a lot as I go along.

Prerequisites: (1) Real Analysis or Linear Analysis, particularly a familiarity with Hilbert space.  Additional knowledge of functional analysis and Fourier analysis wouldn't hurt.  (2) Basic facts about manifolds.  (3) A spirit of adventurousness.