MAT 648: Topics in Quantum Mechanics and Applications
Department of Mathematics
SUNY at Stony Brook
The purpose of this course is to develop further the concepts and
of quantum mechanics, outlined in the Spring 2004 course (see
lecture notes), and to work out some basic applications of quantum
to pure mathematics.
- 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.
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:
Office hours: M, Th 2-3 pm and by appointment.
- Feynman's path integral formalism and related Wiener's theory of
- 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.
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