MAT 648: Advanced Topics in Quantum Mechanics
Fall 2008
Department of Mathematics
Stony Brook University
This course is a continuation of MAT 570
Concepts of Qauntum Mechanics and it is devoted to the functional methods and
supersymmetry.
Schedule: TuTh 12:50-2:10 pm in P-131.
Instructor:
Leon Takhtajan, Math Tower 5-111, email: leontak@math.sunysb.edu Phone:
632-8287,
Office hours: TBA
Topics covered:
- Review of MAT 570
- Feynman's path integral formalism and related Wiener's theory of
functional integration
- Perturbation theory and Feynman diagrams
- Regularized determinants of elliptic operators
- Supersymmetry 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, the basics from
MAT 551, MAT 552, MAT 568, MAT 569. and MAT 570.
Textbook: L. Takhtajan Quantum Mechanics for Mathematicians Amer. Math. Soc. "Graduate Studies in
Mathematics" vol. 95, 2008; Additional Material and Errata.
Topics for presentations:
- Mathematical formulation of quantum mechanics (Chapter 2, § 1)
- Quantization (Chapter 2, §§ 2.1-2.7)
- Stone-von Neumann theorem (Chapter 2, § 3.1)
- Schrödinger operator (Chapter 3, § 1)
- One-dimensional Schrödinger equation and scattering theory (Chapter 3,
§ 2)
- Hydrogen atom and SO(4) (Chapter 3, § 5)
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.www.ehs.stonybrook.edu/fire/disabilities.asp