Date of Award

8-17-2022

Document Type

Thesis

Abstract

We introduce the audience to the mathematics of gauge theory. We begin by formalizing the intuitive concepts of smoothness, tangency, symmetry, constancy, and parallelism. Building up to a theory of parallel transport in associated fiber bundles, we study principal connections in principal bundles as well as the related notions of curvature and holonomy. In particular, we conclude with a non-abelian Stokes's theorem which recasts holonomy in terms of curvature.

Handle

http://hdl.handle.net/11122/13083

Download

Share

COinS