Title: From Harmonic Oscillators to Feynman Diagrams
Speaker: James Carlson
Abstract: The aim of this seminar is to provide mathematicians interested in physics and its interaction with geometry with an understanding of quantum field theory. We begin with a brief review of classical mechanics (Newton's laws and the Lagrangian and Hamiltonian formulation), then give a physically motivated introduction to the Schroedinger equation. This will be followed by an in-depth study of the harmonic oscillator: in isolation, in coupled systems, the perturbation theory thereof, and the use of Feynman diagrams to manage and understand perturbations. The harmonic oscillator will provide a pathway to our treatment of quantum field theory.
This seminar should be accessible to arbitrary mathematics graduate students and postdocs, and to advanced undergraduates with some knowledge of physics, solution of PDE’s via separation of variables, and a passing knowledge of Fourier series and integrals of the kind treated in an engineering mathematics course.
Note: This is a recurring seminar lecture series for the entire Autumn 2016 semester on Tuesdays 11:40 - 12:40 and Thursdays 11:40 - 12:40 all in Cockins Hall 240 starting August 23, 2016 with last date of December 8, 2016