Plane-Symmetric Gauge Field

Abstract

Plane‐symmetric solutions to the gauge field equations are considered on the classical level. The conditions of plane symmetry are gauge‐invariantly defined in terms of the internal holonomy group. It is shown that, if analytic gauge fields satisfy the plane‐symmetry conditions and if there exists at least one source‐free region in event space, then the internal holonomy group is Abelian and a gauge exists in which the gauge field satisfies Maxwell's equations.