The Hamiltonian limit of (3+1)D SU(3) lattice gauge theory on anisotropic lattices

TL;DR

This paper uses path integral Monte Carlo methods to analyze the anisotropic limit of (3+1)D SU(3) lattice gauge theory, demonstrating improved results and universality between Hamiltonian and Euclidean formulations.

Contribution

It introduces a reliable PIMC approach to extract Hamiltonian limit observables, improving upon previous estimates and confirming universality in lattice gauge theories.

Findings

Significant improvement in Hamiltonian estimates

Demonstrates universality between formulations

Validates PIMC as a reliable method

Abstract

The extreme anisotropic limit of Euclidean SU(3) lattice gauge theory is examined to extract the Hamiltonian limit, using standard path integral Monte Carlo (PIMC) methods. We examine the mean plaquette and string tension and compare them to results obtained within the Hamiltonian framework of Kogut and Susskind. The results are a significant improvement upon previous Hamiltonian estimates, despite the extrapolation procedure necessary to extract observables. We conclude that the PIMC method is a reliable method of obtaining results for the Hamiltonian version of the theory. Our results also clearly demonstrate the universality between the Hamiltonian and Euclidean formulations of lattice gauge theory. It is particularly important to take into account the renormalization of both the anisotropy, and the Euclidean coupling $ \beta_E $, in obtaining these results.