Compact QED$_3$ - a simple example of a variational calculation in a gauge theory

TL;DR

This paper demonstrates a variational approach to compact QED in 2+1 dimensions, successfully reproducing key phenomena like mass generation and confinement, serving as a reference for nonabelian gauge theories.

Contribution

It introduces a simple variational method that explicitly preserves gauge invariance and reproduces known results in compact QED, aiding future studies of nonabelian gauge theories.

Findings

Reproduces dynamical mass generation

Shows Polyakov scaling behavior

Confirms nonzero string tension

Abstract

We apply a simple mean field like variational calculation to compact QED in 2+1 dimensions. Our variational ansatz explicitly preserves compact gauge invariance of the theory. We reproduce in this framework all the known results, including dynamical mass generation, Polyakov scaling and the nonzero string tension. It is hoped that this simple example can be a useful reference point for applying similar approximation techniques to nonabelian gauge theories.