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 differential forms and their discrete counterparts ~cochains! provide a natural bridge between the continuum and the lattice versions of the theory, allowing for a natural factorization of the field equations into topological field equations ~i.e., invariant under homeomorphisms! and metric field equations. The various potential sources of inconsistency in the discretization process are identified, distinguished, and discussed. A rationale for a consistent extension of the lattice theory to more general situations, such as to irregular lattices, is considered. © 1999 American Institute of Physics. @S0022-2488~99!02301-4#