Variational estimate of pure gauge field QCD using a lattice Hamiltonian with exact vacuum state

We performed Monte Carlo simulations of pure SU(3) lattice gauge theory using a Hamiltonian having a known vacuum state. A vacuum fixing term which vanishes in the classical continuum limit was added to the Kogut-Susskind Hamiltonian. We variationally estimate glueball mass spectra over a gauge invariant basis and extract the string tension from the area law behavior of these states. We show that in the continuum limit, the vacuum expectation value of the vacuum fixing term does not vanish. In (2+1) dimensions, we calculated string tension and the JPC = 0++ spectrum using a basis consisting of square loops having up to 7 links to a side. Asymptotic scaling is seen in both the string tension and the two lowest-lying 0++ glueball states consistent with published analytic results. String tension in (3+1) dimensions was calculated using square loops up to 7x7 links and yields an exponential scaling window having a different decay constant than the perturbative QCD prediction. Using a basis of square, rectangular, twisted, and bent loops up to 1x2 in size, we find a 0++ state with the same asymptotic scaling behavior as the string tension over a large range of the lattice coupling. A second basis consisting of square, planar loops up to 7x7 links, yields ratio scaling for the lowest 0++ and 2++ eigenstates but not asymptotic scaling. We conclude that the complicated loops are required to accurately represent (3+1)-d glueballs. Mass ratios are in agreement with the alternative Lagrangian approach