On the Gauss Law and Global Charge for QCD

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.