Small coupling (low temperature) expansions of nonabelian Yang-Mills fields on a lattice in temporal gauge

Abstract

A systematic approach to large β expansions of nonabelian lattice gauge theories in temporal gauge is developed. The gauge fields are parameterized by a particular set of coordinates. The main problem is to define a regularization scheme for the infrared singularity that in this gauge appears in the Green's function in the infinite lattice limit. Comparison with exactly solvable two-dimensional models proves that regularization by subtraction of a naive translation invariant Green's function does not work. It suggests to use a Green's function of a half-space lattice first, to place the local observable in this lattice, and to let its distance from the lattice boundary tend to infinity at the end. This program is applied to the Wilson loop correlation function for the gauge group SU(2) which is calculated to second order in 1 β .