# MAT 648: Topics in Quantum Mechanics and Applications

Fall 2004

Department of Mathematics

SUNY at Stony Brook

The purpose of this course is to develop further the concepts and
methods
of quantum mechanics, outlined in the Spring 2004 course (see
the
lecture notes), and to work out some basic applications of quantum
physics
to pure mathematics.

Suggested books:

- Quantum fields and strings: a course for
mathematicians. Vol. 1, 2. Material
from the Special Year on Quantum Field Theory held at the
Institute for Advanced Study, Princeton, NJ, 1996--1997 Eds P. Deligne, P. Etingof, D. Freed, L.
Jeffrey, D. Kazhdan, J. Morgan, D. Morrison and E. Witten.
1999. American Mathematical Society, Providence, RI;
Institute for Advanced Study (IAS), Princeton, NJ.

- Lecture
notes on MAT 570 (this web site).

**Schedule: MW** 10:20-11:40 am, Math. Tower 5-127

**Instructor:** Leon Takhtajan, Math Tower 5-111, Phone:
632-8287,
Office hours: M, Th 2-3 pm and by appointment.

email: *leontak@math.sunysb.edu.*

**Topics covered:**

- Feynman's path integral formalism and related Wiener's theory of
functional integration

- Perturbation theory and Feynman diagrams

- Regularized determinants of elliptic operators

- Sypersymmetry and path integral formalism for fermions
- Path integral derivation of Atiyah-Singer formula for the index
of the Dirac operator and other examples

Prerequisites: The basic core courses curriculum and MAT
551, MAT 552, MAT 568, MAT 569, MAT 570.

** Americans
with Disabilities Act**

**If you have a physical, psychological, medical
or learning disability that
may impact your course work, please contact Disability Support
Services,
ECC (Educational Communications Center) Building, room 128, (631)
632-6748.
They will determine with you what accommodations are necessary and
appropriate. All information and documentation is confidential.
Students requiring emergency evacuation are encouraged to discuss their
needs with their professors and Disability Support Services. For
procedures
and information, go to the following web site:
http://www.ehs.sunysb.edu
**