Group actions on principal bundles and invariance conditions for gauge fields

Abstract

Invariance conditions for gauge fields under smooth group actions are interpreted in terms of invariant connections on principal bundles. A classification of group actions on bundles as automorphisms projecting to an action on a base manifold with a sufficiently regular orbit structure is given in terms of group homorphisms and a generalization of Wang’s theorem classifying invariant connections is derived. Illustrative examples on compactified Minkowski space are given.