Gauge Invariance and Lattice Monopoles

TL;DR

This paper proves that monopoles are gauge-invariant physical objects in lattice gauge theories, despite detection methods depending on the choice of gauge, by deriving from non-abelian Bianchi identities.

Contribution

It establishes the gauge invariance of monopoles and clarifies how detection efficiency varies with abelian projection choices.

Findings

Monopoles are gauge-invariant entities.

Detection methods depend on the abelian projection.

The dependence on gauge choice is well understood.

Abstract

The number and the location of monopoles in Lattice configurations depend on the choice of the gauge, in contrast to the obvious requirement that monopoles, as physical objects, have a gauge-invariant status. It is proved, starting from non-abelian Bianchi identities, that monopoles are indeed gauge-invariant: the technique used to detect them has instead an efficiency which depends on the choice of the abelian projection, in a known and well understood way.