Title: From Harmonic Oscillators to Feynman Diagrams

Time: 10:00-11:30am, every Tuesdays and Thursdays from April 3 to May 3,2016

Venue: 82J04

Description: This short course aims to give a complete introduction to the theory of Feynman diagrams in the simplest possible case: the quartic perturbation of the quantum harmonic oscillator.   Intended for students of mathematics, we will begin with a brief account of the passage from classical to quantum mechanics and a treatment of the quantum mechanical harmonic oscillator.  We will then study perturbations in which the potential function is not quadratic.  The calculation of energies leads naturally to Feynman diagrams.  Time permitting, connections with recent developments in Hodge theory will be discussed.

It is hoped that this course, which should be accessible to advanced undergraduates of mathematics will give some of the background and conceptual vocabulary needed for those interested in the connections between modern physics and mathematics.