MAT 561

General Information

Place and time: MW 11:30am-12:50pm in Physics P128.

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

Office hours: MW 3:00pm-4:30pm in 5-111 and by appointment.

Course description: This is a mathematically rigorous course on mathematical methods of quantum physics. It is a continuation of the last semester course on classical mechanics and classical field theory. We will cover the following topics.

Quantum Mechanics, including Heisenberg, Schrodinger and holomorphic representations and Feynman's path integral formalism.

Quantum Field Theory, including free quantum fields, Fock space, interacting scalar fields and perturbation theory, gauge fields.

Nonperturbative methods, including instanton calculus and other topics (if time permits).

Textbook: We will be using variety of sources for different topics and will indicate the necessary chapters in a due course. The mathematical introduction to quantum mechanics, including the theory of Schrödinger operator, can be found in the second and third chapters of my book Quantum Mechanics for Mathematicians, see alo Errata. For general discussion of the quantization problem, see F.A. Berezin's paper Quantization and for the deformation quantization - the survey Deformation Quantization: Twenty Years After. For mathematical introduction to quantum field theory, see the books by F.A. Berezin, The Method of Second Quantization, by N.N. Bogolyubov, A.A. logunov and I.T. Todorov, Axiomatic Quantum Field Theory, by G.B. Folland Quantum Field Theory: A Tourist Guide for Mathematicians and lectures by J.M. Rabin in Geometry and Quantum Field Theory. For the physics thextbooks, see by N.N. Bogolyubov and N.N. Shirkov Quantum Fields and L.H. Ryder Quantum Field Theory. For rigourous introduction (with complete proofs) to Fock spaces for free quantum fields, Wightman axioms, reconstruction theorem and aanlytic continuation of Wightman functions, see IAS lectures by D. Kazhdan Quantum Field Theory and monograph by N.N. Bogolubov, A.A. Logunov, A.I. Oksak, I.T. Todorov General Principles of Quantum Field Theory. For the introduction to perturbative methods, see Quantum Field Theory of Point Particles and Strings by B. Hatfield and my very old lecture notes.

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.