Path integral Monte Carlo simulations have been performed for U͑1͒ lattice gauge theory in 2ϩ1 dimensions on anisotropic lattices. We extract the static quark potential, the string tension and the low-lying ''glueball'' spectrum. The Euclidean string tension and mass gap decrease exponentially at weak coupling in excellent agreement with the predictions of Polyakov and Göpfert and Mack, but their magnitudes are five times bigger than predicted. Extrapolations are made to the extreme anisotropic or Hamiltonian limit, and comparisons are made with previous estimates obtained in the Hamiltonian formulation.

Using Standard Euclidean Monte Carlo techniques, we discuss in detail the extraction of the glueball masses of 4-dimensional SU(3) lattice gauge theory in the Hamiltonian limit, where the temporal lattice spacing is zero. By taking into account the renormalization of both the anisotropy and the Euclidean coupling, we calculate the string tension and masses of the scalar, axial vector and tensor states using standard Wilson action on increasingly anisotropic lattices, and make an extrapolation to the Hamiltonian limit. The results are compared with estimates from various other Hamiltonian and Euclidean studies. We find that more accurate determination of the glueball masses and the mass ratios has been achieved and the results are a significant improvement upon previous Hamiltonian estimates. The continuum predictions are then found by extrapolation of results obtained from smallest values of spatial lattice spacing. For the lightest scalar, tensor and axial vector states we obtain masses of m 0 ++ = 1654 ± 83 MeV, m 2 ++ = 2272 ± 115 MeV and m 1 +− = 2940 ± 165 MeV, respectively. These are consistent with the estimates obtained in the previous studies in the Euclidean limit. The consistency is a clear evidence of universality between Euclidean and Hamiltonian formulations. From the accuracy of our estimates, we conclude that the standard Euclidean Monte Carlo method is a reliable technique for obtaining results in the Hamiltonian version of the theory, just as in Euclidean case.

We investigate the H-dibaryon, an IðJ P Þ ¼ 0ð0 þ Þ with s ¼ À2, in the chiral and continuum regimes on anisotropic lattices in quenched QCD. Simulations are performed on modest lattices with refined techniques to obtain results with high accuracy over a spatial lattice spacing in the range of a s $ 0:19-0:40 fm. We present results for the energy difference between the ground state energy of the hexa-quark stranglet and the free two-baryon state from our ensembles. A negative energy shift observed in the chirally extrapolated results leads to the conclusion that the measured hexa-quark state is bound. This is further confirmed by the attractive interaction in the continuum limit with the observed H-dibaryon bound by 47 AE 37 MeV.

Standard Monte Carlo simulations have been performed on improved lattices to determine the wave functions and the sizes of the scalar and tensor glueballs at four lattice spacings in the range a = 0.05 − 0.145 fm. Systematic errors introduced by the discretization and the finite volume are studied. Our results in the continuum limit show that the tensor glueball is approximately two times as large as the scalar glueball.PACS numbers: