Loop Equations in Abelian Gauge Theories

TL;DR

This paper explores the loop equations in Abelian gauge theories, presenting an approximation scheme for lattice Maxwell theory that simplifies the analysis of Wilson loops using a geometrical approach.

Contribution

It introduces a novel approximation method for solving loop equations in Abelian gauge theories from a loop-space perspective.

Findings

The approximation yields a partial difference equation in loop variables.

The ansatz reproduces mean field results geometrically.

Provides a new framework for analyzing Wilson loops in lattice gauge theories.

Abstract

The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme for studying these loop-equations for lattice Maxwell theory is presented. The approximation leads to a partial difference equation in the area and length variables of the loop, and certain physically motivated ansatz is seen to reproduce the mean field results from a geometrical perspective.