TG-Equivariance of Connections and Gauge Transformations

TL;DR

This paper introduces a novel perspective on connections on principal bundles by examining the action of the tangential group, leading to new definitions and interpretations of gauge transformations.

Contribution

It provides a new framework for understanding connections and gauge transformations through the lens of the tangential group action.

Findings

New definition of a connection based on TG action

Gauge transformations interpreted as TG effects

Enhanced understanding of principal bundle structures

Abstract

We consider the notion of a connection on a principal bundle $P(M,G)$ from the point of view of the action of the tangential group $TG$. This leads to a new definition of a connection and allows to interpret gauge transformations as effect of the $TG$ action.