MATH 6260, Geometry of Quantum Fields, Fall 2023

Instructor:

Dr. Markus Pflaum

Course Contents:

The course will provide an introduction to the geometric description of quantum field theories. Topics include symplectic mechanics and deformation quantization, classical field theory within the jet bundle formalism, lorentzian geometry, symmetries in quantum mechanics, axioms of a quantum field theory and an outlook to mathematical approaches for rigorous constructions of perturbative and non-perturbative quantum field theories.

Syllabus

Lecture Hours and Venue:

MWF 2:30 pm - 3:20 pm, ECCR 118.

Office Hours:

Mon. 3:30 pm - 4:30 pm, Wed. 10:00 am - 11:00 am, and by appointment

Homework:

Homework assignments will be given here.

Course Project:

In addition to the homework, each student has to work on a course project and write a short paper (around 5 pages) which will be presented in class. A selection of possible topics will be provided here, but you can propose your own project.

Course Grading:

Your grade will be determined from the talk and the course project.

Textbooks:

Folland, G.B., Quantum Field Theory : A Tourist Guide for Mathematicians, AMS (2008).
Takhtajan, L.A., Quantum Mechanics for Mathematicians, AMS (2008).
Streater, R.F. and Wightman, A.S., PCT, Spin, Statistics, and All That, Basic Books.

Online Resources:

The CRing Project
The FANCy Project
The Geometry of Classical and Quantum Fields

Last modified: Sat, August 26, 2023