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

Conserving Lattice Gauge Theory for Finite Systems