Lattice electromagnetic theory from a topological viewpoint

The language of differential forms and topological concepts are applied to study classical electromagnetic theory on a lattice. It is shown that diffe rential forms and their discrete counterparts (cochains) provide a natural bridge between the continuum and the lattice versions of the theory, allowi ng for a natural factorization of the field equations into topological fiel d equations (i.e., invariant under homeomorphisms) and metric field equatio ns. The various potential sources of inconsistency in the discretization pr ocess are identified, distinguished, and discussed. A rationale for a consi stent extension of the lattice theory to more general situations, such as t o irregular lattices, is considered. (C) 1999 American Institute of Physics . [S0022-2488(99)02301-4].