MAT 560

General Information

Place and time: TuTh 1:00-2:20pm in Physics P117.

Professor: Leon Takhtajan, Office: Math Tower 5-111.

Office hours: TuTh 2:30-4:00pm in MAT 5-111 and by appointment.

Course description: This is a mathematically rigorous course on classical (mathematical) physics, with quantum physics being relegated to Part II. We will cover the following topics.

Classical mechanics, including Lagrangian and Hamiltonian formulations, symmetries and solvable systems (planetary motion).

Electromagnetism, including Maxwell equations in a relativistic form, geometric interpretation as U(1) gauge theory, exact solutions: propagating waves, monopoles, instantons.

Special relativity, Lorentz and Poincare groups.

Classical field theory, including scalar and vector fields, sigma models and gauge theories (Yang-Mills theory).

The theory of gravity, a mathematical instroduction.

Textbook: We will be using variety of sources for different topics and will indicate the necessary chapters in a due course. The concise mathematical introduction to classical mechanics can be found in the first chapter of my book Quantum Mechanics for Mathematicians. On p. 60 one finds classic references on the subject, including Mechanics by L.D. Landau and E.M. Lifshitz. Foor topics in eltrodynamics we will be using textbook Introduction to Electrodynamics David J. Griffiths and The Classical Theory of Fields by L.D. Landau and E.M. Lifshitz. For classical field theory also see the chapter Classical field theory by P. Deligne and D. Freed in Quantum Fields and Strings: A Course for Mathematicians.

Homework: there will be several homework sets during the semester, aimed at mastering the course material. HW 1, HW 2, HW 3.

Grading: Throughout the semester students will be expected to present homework solutions in class. The course grade will be determined by these presentations and the participation in the class.

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.