Geometrical formalism in gauge theories

TL;DR

This paper reviews the geometrical formalism of gauge theories, focusing on invariant connections, bundle classification, and applications to dimensional reduction, providing insights relevant for quantization.

Contribution

It offers a comprehensive review of the geometrical formalism in gauge theories, including invariant connections and bundle classification, with new results on bundles over two-dimensional spaces.

Findings

Analysis of invariant connections in gauge theories

Classification results for principal fibre bundles over 2D spaces

Applications to coset space dimensional reduction

Abstract

We review the basic elements of the geometrical formalism for description of gauge fields and the theory of invariant connections, and their applications to the coset space dimensional reduction of Yang-Mills theories. We also discuss the problem of classification of principal fibre bundles, which is important for the quantization of gauge theories. Some results for bundles over two-dimensional spaces are presented.