Using Standard Euclidean Monte Carlo techniques, we discuss in detail theextraction of the glueball masses of 4-dimensional SU(3) lattice gauge theoryin the Hamiltonian limit, where the temporal lattice spacing is zero. By takinginto account the renormalization of both the anisotropy and the Euclideancoupling, we calculate the string tension and masses of the scalar, axialvector and tensor states using standard Wilson action on increasinglyanisotropic lattices, and make an extrapolation to the Hamiltonian limit. Theresults are compared with estimates from various other Hamiltonian andEuclidean studies. We find that more accurate determination of the glueballmasses and the mass ratios has been achieved and the results are a significantimprovement upon previous Hamiltonian estimates. The continuum predictions arethen found by extrapolation of results obtained from smallest values of spatiallattice spacing. For the lightest scalar, tensor and axial vector states weobtain masses of $m_{0^{++}}=1654 \pm 83$ MeV, $m_{2^{++}}=2272\pm 115$ MeV and$m_{1^{+-}}=2940\pm 165$ MeV, respectively. These are consistent with theestimates obtained in the previous studies in the Euclidean limit. Theconsistency is a clear evidence of universality between Euclidean andHamiltonian formulations. From the accuracy of our estimates, we conclude thatthe standard Euclidean Monte Carlo method is a reliable technique for obtainingresults in the Hamiltonian version of the theory, just as in Euclidean case.
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