On Symmetric Gauge Fields for arbitrary Gauge and Symmetry Groups

TL;DR

This paper classifies symmetric principal bundles with compact gauge and symmetry groups on foliated manifolds, generalizes Wang's theorem for invariant connections, and provides explicit local gauge potentials.

Contribution

It introduces a comprehensive classification of symmetric bundles and extends Wang's theorem to broader settings with explicit local expressions.

Findings

Classification of symmetric principal bundles with compact groups

Generalization of Wang's theorem for invariant connections

Explicit local gauge potentials for invariant connections

Abstract

A classification of the possible symmetric principal bundles with a compact gauge group, a compact symmetry group and a base manifold which is regularly foliated by the orbits of the symmetry group is derived. A generalization of Wang's theorem (classifying the invariant connections) is proven and local expressions for the gauge potential of an invariant connection are given.