 |
MAT 561 Mathematical Physics II Spring 2026 |
| Place and time: TuTh 11:00am-12:20pm in
Earth & Space 183 |
| Instructor: Leon Takhtajan, Office: Math Tower 5-111 |
| Office hours: Tu 1:30pm-2:30pm and W 2:00pm-4:00pm. |
| Course description: This is a mathematically rigourous
course on quantum (mathematical)
physics, a continuation of the last semester course
Mathematical
Physics I on classical
mechanics and classical field theory. We will
cover the following topics, illustrated by applications to
analysis, geometry and topology.
- Review of classical mechanics.
- Quantum Mechanics as quantization of classical mechanics.
- Heisenberg commutation relations and Stone-von Neumann theorem.
- Feynman path integral.
- Fermion systems as quantization of classical mechanics with
anticommuting variables.
- Feynman path integrals over anticommuting variables.
- Supersymmetry.
- Introduction to Quantum Field Theory.
- Free bose and fermi quantum fields, Fock spaces.
- Interacting quantum fields.
- Quantization of the gauge fields.
- Supersymmetric Yang-Mills theory and Donaldson invariants.
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| Textbook: There will be no assigned
textbooks; I will use various sources, including lecture notes
from the last semester (a book with Alexander Kirillov Classical
field theory for mathematicians, to be published by the AMS in
2026) and my book on QM (check
this site for typos and corrections). Class lecture notes will
be posted and updated below.
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| Disability support services. If you have a physical, psychological, medical or learning
disability that may impact your course work, please contact
Disability Support Services, 128 ECC Building (631)
632-6748. They will determine with you what accommodations are
necessary and appropriate. All information and documentation
is confidential. 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 who require assistance during
emergency evacuation are encouraged to discuss their needs
with their professors and Disability Support Services. |
| Academic integrity.
Each student must pursue his or her academic goals honestly and be
personally accountable for all submitted work. Representing
another person's work as your own is always wrong.
Faculty is required to report any suspected instances of
academic dishonesty to the Academic Judiciary.
Faculty in the Health Sciences Center (School of Health
Technology
& Management, Nursing, Social Welfare, Dental Medicine) and
School of Medicine are required to follow their
school-specific procedures.
For more comprehensive information on academic integrity,
including categories of academic dishonesty please refer to
the academic judiciary website. |
| Critical incident management.
Stony Brook University expects students to respect the rights, privileges, and property of other people. Faculty are required to report to the Office of University Community Standards any disruptive behavior that interrupts their ability to teach, compromises the safety of the learning environment, or inhibits students' ability to learn. Faculty in the HSC Schools and the School of Medicine are required to follow their school-specific procedures. Further information about most academic matters can be found in the Undergraduate Bulletin, the Undergraduate Class Schedule, and the Faculty-Employee Handbook. |
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