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Discrete Gauge Theories

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Particles and Fields

Part of the book series: CRM Series in Mathematical Physics ((CRM))

Abstract

We present a self-contained treatment of planar gauge theories broken down to some finite residual gauge group H via the Higgs mechanism. The main focus is on the discrete H gauge theory describing the long-distance physics of such a model. The spectrum features global H charges, magnetic vortices, and dyonic combinations. Due to the AharonovBohm effect, these particles exhibit topological interactions. Among other things, we review the Hopf algebra related to this discrete H gauge theory, which provides a unified description of the spin, braid, and fusion properties of the particles in this model. Exotic phenomena such as flux metamorphosis, Alice fluxes, Cheshire charge, (non-)Abelian braid statistics, the generalized spin-statistics connection, and non-Abelian AharonovBohm scattering are explained and illustrated by representative examples.

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Authors
  1. Mark Wild de Propitius
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  2. F. Alexander Bais
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Editors and Affiliations

  1. Department of Physics and Astronomy, University of British Columbia, Vancouver, British Columbia, V6T 1Z1, Canada

    Gordon Semenoff

  2. Centre de Recherches Mathématiques, Université de Montréal, Montreal, Québec, H3C 3J7, Canada

    Luc Vinet

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de Propitius, M.W., Bais, F.A. (1999). Discrete Gauge Theories. In: Semenoff, G., Vinet, L. (eds) Particles and Fields. CRM Series in Mathematical Physics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1410-6_8

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  • DOI: https://doi.org/10.1007/978-1-4612-1410-6_8

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