Principal bundles and connections modelled by Lie group bundles

TL;DR

This paper extends the theory of principal bundles by using Lie group bundles to model connections and explores their properties, with applications to gauge theories and a reinterpretation of the Utiyama Theorem.

Contribution

It introduces a generalized framework for principal bundles using Lie group bundles and defines equivariant connections within this context, advancing geometric gauge theory.

Findings

Established existence conditions for equivariant connections.

Provided new examples illustrating the theory.

Revisited the Utiyama Theorem from a Lie group bundle perspective.

Abstract

In this work, generalized principal bundles modelled by Lie group bundle actions are investigated. In particular, the definition of equivariant connections in these bundles, associated to Lie group bundle connections, is provided, together with the analysis of their existence and their main properties. The final part gives some examples. In particular, since this research was initially originated by some problems on geometric reduction of gauge field theories, we revisit the classical Utiyama Theorem from the perspective investigated in the article.