Abelian Projections and Monopoles

Abstract

The monopole confinement mechanism in the abelian projection of lattice gluodynamics is reviewed. The main topics are: the abelian projection on the lattice and in the continuum, a numerical study of the abelian monopoles in the lattice gauge theory. Additionally, we briefly review the notation of differential forms, duality, and the BKT transformation in the lattice gauge theories.

34 pages, LaTeX, 23 figures, uses epsf.sty and epsfig.sty; Lectures given by Mikhail Polikarpov at the Workshop "Confinement, Duality and Non-Perturbative Aspects of QCD", Cambridge (UK), 24 June - 4 July 1997; figures are rearranged

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• Universality check of Abelian Monopoles
• Finite Temperature QCD with Two Flavors of Non-perturbatively Improved Wilson Fermions
• The Casimir effect and deconfinement phase transition
• Center vortices as sources of Abelian dominance in pure SU(2) Yang-Mills theory
• Analytic derivation of dual gluons and monopoles from SU(2) lattice Yang-Mills theory. II. Spin foam representation
• How to get rid of Dirac worldsheets in the Cho-Fadeev-Niemi representation of SU(2) Yang-Mills theory
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• Analytic derivation of dual gluons and monopoles from SU(2) lattice Yang-Mills theory. I. BF Yang-Mills representation
• A non Abelian effective model for ensembles of magnetic defects in QCD(3)
• Ultraviolet Behavior of the Gluon Propagator in the Maximal Abelian Gauge
• Color confinement and restoration of residual local gauge symmetries
• Chaotic monopole interactions and vacuum disorder