Localization and symmetries

TL;DR

This paper investigates the relationship between symmetries and charges in gauge theories, providing non-perturbative insights into charge conservation, the Higgs mechanism, and axial symmetry in QCD.

Contribution

It offers a non-perturbative analysis of charge commutators, clarifies the Higgs phenomenon, and examines axial symmetry conservation in QCD.

Findings

Correct expression for electric charge on Coulomb states

Absence of Goldstone bosons and massless vector bosons in broken symmetry

Compatibility of axial current conservation with eta' mass

Abstract

The violation of the Noether relation between symmetries and charges is reduced to the time dependence of the charge associated to a conserved current. For the U(1) gauge symmetry a non-perturbative control of the charge commutators is obtained by an analysis of the Coulomb charged fields. From this, in the unbroken case we obtain a correct expression for the electric charge on the Coulomb states, its superselection and the presence of massless vector bosons; in the broken case, we obtain a general non-perturbative version of the Higgs phenomenon, i.e. the absence of massless Goldstone bosons and of massless vector bosons. The conservation of the (gauge dependent) current associated to the U(1) axial symmetry in QCD is shown to be compatible with the time dependence of the corresponding charge commutators and a non-vanishing eta' mass, as a consequence of the non locality of the (conserved) current.