Non-Abelian discrete gauge theory

Author: Lee, Kai-Ming

Year: 1994

Degree: Dissertation (Ph.D.)

Advisor: Preskill, John P.

Committee Member: Unknown, Unknown

Option: Physics

DOI: 10.7907/KCB0-S712

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 "wormhole" 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.

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