Measure of the path integral in lattice gauge theory

TL;DR

This paper develops a new measure for the path integral in lattice gauge theory that includes an additional factor, enabling accurate calculation of single transition amplitudes crucial for partition functions and free energy computations.

Contribution

It introduces a modified measure for lattice gauge theory path integrals, extending beyond the Haar measure, and demonstrates its effectiveness through numerical simulations for U(1) gauge theory.

Findings

The new measure accurately computes single transition amplitudes.

Numerical results agree with Hamiltonian evolution.

The method improves calculations of partition functions.

Abstract

We show how to construct the measure of the path integral in lattice gauge theory. This measure contains a factor beyond the standard Haar measure. Such factor becomes relevant for the calculation of a single transition amplitude (in contrast to the calculation of ratios of amplitudes). Single amplitudes are required for computation of the partition function and the free energy. For U(1) lattice gauge theory, we present a numerical simulation of the transition amplitude comparing the path integral with the evolution in terms of the Hamiltonian, showing good agreement.