On Nonlinear Gauge Theories

TL;DR

This paper explores nonlinear gauge theories using Lie groupoids, deriving a generalized gauge transformation formula that extends classical Yang-Mills theory, bridging mathematical structures with physical applications.

Contribution

It introduces a novel formulation of gauge transformations in principal bundles with Lie groupoids, generalizing classical Yang-Mills gauge theories.

Findings

Derived a new gauge transformation formula for Lie groupoid-based gauge theories.

Established the relation between the mathematical framework and existing physics literature.

Extended classical gauge theory concepts to nonlinear, groupoid-based contexts.

Abstract

In this note, we study non-linear gauge theories for principal bundles, where the structure group is replaced by a Lie groupoid. We follow the approach of Moerdijk-Mrcun and establish its relation with the existing physics literature. In particular, we derive a new formula for the gauge transformation which closely resembles and generalizes the classical formulas found in Yang Mills gauge theories.