Reaching the continuum limit in lattice gauge theory - without a computer

TL;DR

This paper analytically derives the scaling behavior of the mass gap in 2+1 dimensional U(1) lattice gauge theory using Hamiltonian methods, showing agreement with numerical results without relying on computational simulations.

Contribution

It introduces an analytical approach to determine the continuum limit scaling in lattice gauge theory using plaquette expansion and Hamiltonian formalism.

Findings

Analytical scaling slope of the mass gap matches numerical results.

Scaling behavior is demonstrated across the strong to weak coupling transition.

Results validate the plaquette expansion method in Hamiltonian lattice gauge theory.

Abstract

The scaling slope of the anti-symmetric mass gap M of compact U(1)_{2+1} lattice gauge theory is obtained analytically in the Hamiltonian formalism using the plaquette expansion. Based on the first four moments of the Hamiltonian with respect to a one-plaquette mean field state the results demonstrate clear scaling of M at and beyond the transition from strong to weak coupling. The scaling parameters determined agree well with the range of numerical determinations available.