Quark confinement in lattice gauge theory

Abstract

We review Wilson``s lattice gauge theory. The action is defined on the discrete lattice keeping the invariance under local gauge transformation. The gauge variables are treated as angular variables in Abelian gauge theory. We compute correlation function at the two extreme limits of the coupling constant. We find ``area law`` at strong coupling and ``perimeter law`` at weak coupling. The area law is characteristic of quark confinement. There is a phase transition in Abelian gauge theory. We find the gauge field undergoes a first order phase transition using mean field approximation. In non-Abelian gauge theory the gauge variables enter the action through rotation matrices. Quark confining phase exists at all couplings in non-Abelian gauge theory.