Monday and Wednesday 4:10-5:25pm

Mathematics 307

This course will be an introduction to quantum field theory aimed at mathematicians,

although physicists may also find it of interest. It will emphasize fundamental

issues in quantum field theory and concentrate on some simple examples, mainly

in two space-time dimensions, leading to an examination of some of the quantum

field theories that have been of most mathematical interest.

Prerequisites: Modern geometry at the level of a first year graduate math course

(bundles, connections, curvature), some knowledge of Lie groups and their

representations, some physics background (classical mechanics and electromagnetism,

quantum mechanics).

(Very) Tentative (and highly overambitious) Syllabus

Lecture Notes

Introduction and Suggested Reading

Hamiltonian Mechanics and Symplectic Geometry

Problem Sets

There will be two problem sets for the course, which should

be handed in by anyone registered for the course who needs

a letter grade.

Problem Set 1:

From Orlando Alvarez, Lectures on Quantum Mechanics and

the Index Theorem, IAS/Park City, 1991. See me for copies

of this.

Exercises 2.2, 2.4 (parts 1-5), 5.2, 5.3, 5.4, 5.5, 6.2

Problem Set 2:

From Anthony Zee, Quantum Field Theory in a Nutshell, Princeton, 2003.

Work out the following exercises:

I.3.1, I.3.2, I.8.3, I.8.4, I.9.1, II.1.10, II.2.1, IV.5.2, IV.5.3