On the Gauss Law and Global Charge for QCD

TL;DR

This paper explores the local Gauss law in lattice QCD, revealing a gauge invariant, additive ${ m Z}_3$-valued global charge linked to boundary flux, with implications for continuous QCD.

Contribution

It demonstrates that the local Gauss law in lattice QCD implies a gauge invariant ${ m Z}_3$-valued global charge related to boundary flux.

Findings

Global charge is ${ m Z}_3$-valued and gauge invariant.

Total charge equals boundary flux of a ${ m Z}_3$-valued quantity.

Implications discussed for continuous QCD.

Abstract

The local Gauss law of quantum chromodynamics on a finite lattice is investigated. It is shown that it implies a gauge invariant, additive law giving rise to a gauge invariant ${\mathbb Z}_3$-valued global charge in QCD. The total charge contained in a region of the lattice is equal to the flux through its boundary of a certain ${\mathbb Z}_3$-valued, additive quantity. Implications for continuous QCD are discussed.