MAT 570: Concepts of Quantum Mechanics
Spring 2007
Department of Mathematics
SUNY at Stony Brook
The purpose of this course, which is the part of the RTG program, is to
introduce mathematics students to the basic concepts and methods of
quantum physics, including sypersymmetry and Feynman's path integral,
which
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
mathematics students.
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.
Schedule: TuTh 11:20-12:40 pm, Math Tower 5-127
Instructor: Leon Takhtajan, Math Tower 5-111, Phone:
632-8287,
Office hours TBA.
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
Prerequisites: The basic core courses curriculum and MAT
551, MAT 552, MAT 568, MAT 569. All necessary facts from the theory of operators
in Hilbert spaces can be found in the last three monographs for the list of suggested
books.
DSS advisory. If you have a physical,
psychological,
medical, or learning disability that may affect your course work,
please contact Disability Support
Services (DSS) office: ECC (Educational Communications Center)
Building, room 128, telephone (631) 632-6748/TDD.
DSS will determine with you what accommodations are necessary and
appropriate. Arrangements should be made early in the semester (before
the first exam) so that your needs can be accommodated. All information
and documentation of disability
is confidential.
Students requiring emergency evacuation are encouraged to discuss their
needs with
their professors and DSS. For procedures and information, go to the
following web site http://www.ehs.sunysb.edu
and search Fire safety and
Evacuation and Disabilities.