Lie Groupoids in Classical Field Theory II: Gauge Theories, Minimal Coupling and Utiyama's Theorem

TL;DR

This paper develops a novel framework for classical gauge theories using Lie groupoids and algebroids, extending the concept of symmetry to local transformations and addressing minimal coupling and Utiyama's theorem.

Contribution

It introduces a Lie groupoid-based formalism for gauge theories, providing a new mathematical approach to local symmetries in classical field theory.

Findings

Extended the Lie groupoid formalism to gauge theories

Addressed minimal coupling within the new framework

Connected the approach to Utiyama's theorem

Abstract

In the two papers of this series, we initiate the development of a new approach to implementing the concept of symmetry in classical field theory, based on replacing Lie groups/algebras by Lie groupoids/algebroids, which are the appropriate mathematical tools to describe local symmetries when gauge transformations are combined with space-time transformations. In this second part, we shall adapt the formalism developed in the first paper to the context of gauge theories and deal with minimal coupling and Utiyama's theorem.