Department of Mathematics

SUNY at Stony Brook

Suggested books

- Geometry and
quantum field theory.
Lecture notes from the Summer School on the Geometry and Topology of
Manifolds and Quantum Field Theory held in Park City, Utah, June
22--July 20, 1991 Eds D. Freed and K. Uhlenbeck,
*American Mathematical Society, Providence, RI; Institute for Advanced Study (IAS), Princeton, NJ,*1995.

- 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.

- Mackey, George W. The mathematical foundations of quantum
mechanics.
A lecture-note volume.
Reprint of the 1963 original. Mathematical
Physics Monograph Series.
*Benjamin/Cummings Publishing Co., Inc., Advanced Book Program, Reading, Mass.,*1980

**Schedule: TuTh** 2:20-3:40 pm, Harriman Hall 115

**Instructor:** Leon Takhtajan, Math Tower 5-111, Phone:
632-8287,
Office hours Tu W 4-5 pm.

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

**Topics covered:**

- Mathematical methods of classical mechanics, including Lagrangian
and Hamiltonian formalisms, symmetries and conservation laws

- Mathematical foundation of quantum mechanics, including
Heisenberg, Schrodinger and holomorphic representations and deformation
quantization

- 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 (if time permits)

Prerequisites:

**Take-Home Final Exam: (due Monday, May 10 in 5-111, or earlier in
class).
**

** 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.www.ehs.stonybrook.edu/fire/disabilities.asp
**