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We investigate (2+1)-d Hamiltonian lattice gauge theory using a class ofHamiltonians having exactly known vacuum states. These theories are shown tohave a wide range of possible classical continuum limits which differ from thatof the standard Kogut-Susskind Hamiltonian. This conclusion is at variance withsome previously published results. We examine the quantum continuum behavior ofthese theories by both analytic and numerical methods including plaquette spaceintegration and standard Monte Carlo techniques. String tension and variationalestimates for the $J^{\rm PC}=0^{++}$ glueball spectra are presented for SU(3).We find that in spite of the wide range of classical behavior predicted, thesetheories correspond to only two distinct quantum systems in the weak couplinglimit. One of these quantum limits gives string tensions and glueball stateswhich show scaling in weak coupling which agrees with the perturbativeprediction for the (2+1)-d problem.Comment: KITCS93-12-2, 28 pages (REVTeX) plus 11 postscript figures all  uuencoded. (Modifications: Expanded introductory section and references plus  other minor changes.

Hamiltonian SU(N) lattice gauge theories with exact vacuum states in 2+1 dimensions