U(1) gauge theory on a torus

Abstract

U(1) gauge theory with the Villain action on a cubic lattice approximation of three- and four-dimensional torus is considered. As the lattice spacing approaches zero, provided the coupling constant correspondingly approaches zero, the naturally chosen correlation functions converge to the correlation functions of the R-gauge electrodynamics on three- and four-dimensional torus. When the torus radius tends to infinity these correlation functions converge to the correlation functions of the R-gauge Euclidean electrodynamics.

Supported by the Russian Foundation of Fundamental Researches under Grant 93011-147.