Path integral Monte Carlo approach to the U(1) lattice gauge theory in 2+1 dimensions

Abstract

Path integral Monte Carlo simulations have been performed for U(1) lattice gauge theory in 2+1 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 G\"opfert 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.