Conserving Lattice Gauge Theory for Finite Systems

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 $\mathcal{O}(a)$ 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.

Comments: 9 pages, 3 figures; computations in the Abelian setting provided as ancillary Mathematica notebooks