Non-Abelian discrete gauge theory

Abstract

Gauge theory with a finite gauge group (or with a gauge group that has disconnected components) is systematically studied, with emphasis on the case of a non-Abelian gauge group. An operator formalism is developed, and an order parameter is constructed that can distinguish the various phases of a gauge theory. The non-Abelian Aharonov-Bohm interactions and holonomy interactions among cosmic string loops, vortices, and charged particles are analyzed; the detection of Cheshire charge and the transfer of charge between particles and string loops (or vortex pairs) are described. Non-Abelian gauge theory on a surface with non-trivial topology is also discussed. Interactions of vortices with handles on the surface are discussed in detail. The electric charge of the mouth of a and the magnetic flux linked by the wormhole are shown to be non-commuting observables. This observation is used to analyze the color electric field that results when a colored object traverses a wormhole.