MAT 560: Mathematical Physics I
Fall 2025
- Classical mechanics, including Lagrangian and Hamiltonian formulations, symmetries and integrable systems (planetary motion).
- Classical field theory, including scalar and vector fields, sigma models and gauge theories (Yang-Mills theory). Electromagnetism as U(1) gauge field theory.
- Chern--Simons topological theory (time permitting)
Our main reference will be the following manuscript (soon to be published):
Classical field theory for mathematicians, by A. Kirillov and L. Takhtadjan
Additional references:
Classical mechanics:
- Quantum Mechanics for Mathematicians, by Leon Takhtajan; the first chapter is available online at math.sunysb.edu/~leontak/CM.pdf.
- Mathematical Methods of Classical Mechanics, by V. Arnold
- Introduction to Classical Field Theory, by Charles Torre
- Classical Field Theory, by Horatiu Nastase
Information for students with disabilities: If you have a physical, psychological, medical, or learning disability that may impact your course work, please contact Disability Support Services at (631) 632-6748 or http://studentaffairs.stonybrook.edu/dss/. They will determine with you what accommodations are necessary and appropriate. All information and documentation is confidential.
Students who require assistance during emergency evacuation are encouraged to discuss their needs with their professors and Disability Support Services. For procedures and information go to the following website: http://www.sunysb.edu/ehs/fire/disabilities.shtml