On the Gauss law and global charge for quantum chromodynamics

Abstract

The local Gauss law of quantum chromodynamics (QCD) on a finite lattice is investigated. It is shown that it implies a gauge invariant, additive law giving rise to a gauge invariant Z3-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 Z3-valued, additive quantity. Implications for continuum QCD are discussed.