Monopoles, abelian projection, and gauge invariance

Understand

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.