Conserving Lattice Gauge Theory for Finite Systems

TL;DR

This paper introduces a new lattice gauge theory action suitable for finite systems with non-periodic boundaries, ensuring proper Gauss' law, symmetric energy-momentum tensor, and automatic ${ m O}(a)$ improvement, demonstrated with Abelian gauge theory.

Contribution

A novel lattice gauge theory action for finite systems that incorporates non-periodic boundary conditions and improves numerical properties.

Findings

Constructed an action implementing Gauss' law correctly.

Achieved symmetric energy-momentum tensor.

Demonstrated ${ m O}(a)$ improvement in Abelian gauge theory.

Abstract

In this contribution I discuss a recent proposal of a novel action for lattice gauge theory for finite systems, which accommodates non-periodic spatial boundary conditions. Drawing on the summation-by-parts formulation of finite differences and finite volume strategies of computational electrodynamics, an action is constructed that implements the proper integral form of Gauss' law and exhibits an inherently symmetric energy momentum tensor, all while realizing automatic ${\cal O}(a)$ improvement. Its central ingredients are illustrated using Abelian gauge theory as example.