Lecture 22 - Local Representations of a Connection on the Base Manifold: Yang-Mills Fields (Schuller's Geometric Anatomy of Theoretical Physics)

Video Lecture:

Summary of contents: Yang-Mills field as pull-back of a connection one form along a local section; local trivialisations of a principal bundle; local representation of a connection one-form; Maurer-Cartan form; example: the Yang-Mills fields on the frame bundle, Christoffel symbol; example: calculation of the Maurer-Cartan form of the general linear group GL(n,R); patching Yang-Mills fields on different domains; the gauge map; example: the gauge map on the frame bundle.

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Lecture Notes for this lecture: