Conserving Lattice Gauge Theory for Finite Systems

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.