Some results on topological currents in field theory

TL;DR

This paper presents exact results on topological currents in field theories, showing that topological charges do not generate symmetries and that superconductivity via the Anderson-Higgs mechanism requires minimal gauge coupling.

Contribution

It proves that topological charges cannot generate symmetry transformations and establishes conditions for superconductivity related to gauge coupling.

Findings

Topological charges do not generate symmetry transformations.

Superconductivity via Anderson-Higgs requires minimal gauge coupling.

Topological origin of certain charges is established.

Abstract

A few exact results concerning topological currents in field theories are obtained. It is generally shown that, a topological charge can not generate any kind of symmetry transformation on the fields. It is also proven that, the existence of a charge that does not generate any kind of symmetry transformation on the fields, has to be of topological origin. As a consequence, it is found that in a given theory, superconductivity via Anderson-Higgs route can only occur if the gauge coupling with other fields is minimal. Several physical implications of these results are studied.