MAT 570: Concepts of Quantum Mechanics
Department of Mathematics
SUNY at Stony Brook
The purpose of this course is to
introduce mathematics students to the basic concepts and methods of
quantum physics, including sypersymmetry and Feynman's path integral,
play a profound role in geometry, topology, and other areas of
mathematics. For the physics students, the course may serve as a
(rather simplified) "dictionary" between mathematical and physical
"languages". No prior knowledge of physics will be assumed for
- 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.
Schedule: TuTh 2:20-3:40 pm, Harriman Hall 115
Instructor: Leon Takhtajan, Math Tower 5-111, Phone:
Office hours Tu W 4-5 pm.
- 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
- 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 (if time permits)
Prerequisites: The basic core courses curriculum and MAT
551, MAT 552, MAT 568, MAT 569.
Take-Home Final Exam: (due Monday, May 10 in 5-111, or earlier in
with Disabilities Act
If you have a physical, psychological, medical
or learning disability that
may impact your course work, please contact Disability Support
ECC (Educational Communications Center) Building, room 128, (631)
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
and information, go to the following web site: