Quantum Field Theory and Geometry: Mathematics G6434

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