Local observables in non-abelian gauge theories

Labelling of the physical states of a non-abelian gauge theory on a lattice in terms of local observables is considered. The labelling is in terms of local color electric field observables and (separately) local color magnetic field observables. Matter fields are also included. Non-local observables required when space is multiply connected, are specified. The non-abelian version of Stokes' theorem is considered. Relevance to the continuum theory is discussed in detail.