ar X iv : h ep - l at / 0 50 10 26 v 2 3 1 Ja n 20 05 NSF - KITP - 05 - 04 BCCUNY - HEP / 05 - 01 LATTICE ( QCD )

We consider a 2 + 1-dimensional SU(N) lattice gauge theory in an axial gauge with the link field U 1 set equal to one. The term in the Hamiltonian containing the square of the electric field in 1-direction is non-local. Despite this non-locality, we show that weak-coupling perturbation theory in this term gives a finite vacuum-energy density to second order, and suggest that this property holds to all orders. Heavy quarks are confined, the spectrum is gapped, and the space-like Wilson loop has area decay.