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 conservation laws, symmetry, and improved accuracy, based on finite difference and electrodynamics strategies.

Contribution

It develops a novel, conserving lattice gauge theory action for finite systems that handles boundary conditions and improves accuracy, extending previous methods.

Findings

The new action accommodates non-periodic boundary conditions.

It enforces Gauss' law in the discretized setting.

The formulation exhibits an inherently symmetric energy-momentum tensor.

Abstract

In this study I develop a novel action for lattice gauge theory for finite systems, which accommodates non-periodic boundary conditions, implements the proper integral form of Gauss' law and exhibits an inherently symmetric energy momentum tensor, all while realizing automatic ${\cal O}(a)$ improvement. Taking the modern summation-by-parts formulation for finite differences as starting point and combining it with insight from the finite volume strategies of computational electrodynamics I show how the concept of a conserving discretization can be realized for non-Abelian lattice gauge theory. Major steps in the derivation are illustrated using Abelian gauge theory as example.