# Gauge Theories and Fibre Bundles - Applications to Particle Dynamics

## TL;DR

This paper explores the geometric structures of gauge theories using fibre bundles, highlighting their impact on physical phenomena like instantons and monopoles, and aims to introduce physicists to these mathematical concepts.

## Contribution

It provides an accessible introduction to fibre bundles and their relevance to gauge theories for physicists, emphasizing global geometric effects on physics.

## Key findings

- Global geometric properties influence physical phenomena such as instantons and monopoles.
- Fibre bundles provide a mathematical framework for understanding gauge theories.
- Geometric structures can lead to phenomena like CP-violation and fermion creation.

## Abstract

The underlying mathematical structures of gauge theories are known to be geometrical in nature and the local and global features of this geometry have been studied for a long time in mathematics under the name of fibre bundles. It is now understood that the global properties of gauge theories can have a profound influence on physics. For example, instantons and monopoles are both consequences of properties of geometry in the large, and the former can lead to, e.g., CP-violation, while the latter can lead to such remarkable results as the creation of fermions out of bosons. Some familiarity with global differential geometry and fibre bundles seems therefore very desirable to a physicist who works with gauge theories. One of the purposes of the present work is to introduce the physicist to these disciplines using simple examples.