Monopoles, abelian projection, and gauge invariance

Details Monopoles, abelian projection, and gauge invariance Monopoles, abelian projection, and gauge invariance

2010-02-22

arxiv.org/abs/1002.3874v2

Phys.Rev.D81:085022,2010

Physics

High Energy Physics

High Energy Physics - Lattice

9 pages, no figure

Scientific paper

10.1103/PhysRevD.81.085022

A direct connection is proved between the Non-Abelian Bianchi Identities(NABI), and the abelian Bianchi identities for the 't Hooft tensor. As a consequence the existence of a non-zero magnetic current is related to the violation of the NABI's and is a gauge-invariant property. The construction allows to show that not all abelian projections can be used to expose monopoles in lattice configurations: each field configuration with non-zero magnetic charge identifies its natural projection, up to gauge transformations which tend to unity at large distances. It is shown that the so-called maximal-abelian gauge is a legitimate choice. It is also proved, starting from the NABI, that monopole condensation is a physical gauge invariant phenomenon, independent of the choice of the abelian projection.

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