Year: 2015
Type: preprint
Abstract: This paper provides a pedagogical introduction to the quantum mechanical path integral and its use in proving index theorems in geometry, specifically the Gauss-Bonnet-Chern theorem and Lefschetz fixed point theorem. It also touches on some other important concepts in mathematical physics, such as that of stationary phase, supersymmetry and localization. It is aimed at advanced undergraduates and beginning graduates, with no previous knowledge beyond undergraduate quantum mechanics assumed. The necessary mathematical background in differential geometry is reviewed, though a familiarity with this material is undoubtedly helpful.
Source: arXiv (Cornell University)
Author: van Loon, Mark
Institution: University of Oxford
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2286907967