Analytic calculation of the mass gap in U(1)_{2+1} lattice gauge theory

TL;DR

This paper analytically calculates the photon mass gap in 2+1 dimensional U(1) lattice gauge theory using Hamiltonian moments and plaquette expansion, showing clear scaling behavior consistent with numerical results.

Contribution

It introduces an analytic approach using Hamiltonian moments and plaquette expansion to compute the mass gap, providing insights into the scaling behavior across coupling regimes.

Findings

Scaling of the mass gap is evident at and beyond the transition.

Analytic results agree well with numerical calculations.

Method provides a new way to analyze lattice gauge theories.

Abstract

An analytic calculation of the photon mass gap M of compact U(1)_{2+1} in the Hamiltonian formalism is performed utilizing the first four Hamiltonian moments with respect to a one-plaquette mean field state in the plaquette expansion method. Scaling of M is clearly evident at and beyond the transition from strong to weak coupling. The scaling behaviour agrees well with the range of results from numerical calculations.