On the Axioms of Topological Electromagnetism

TL;DR

This paper refines the axioms of topological electromagnetism using advanced mathematical tools, explores the constitutive law's role in spacetime structure, and discusses implications for wave motion.

Contribution

It introduces de Rham homology of k-vector fields and replaces Hodge duality with Poincare duality in topological electromagnetism.

Findings

Refined axioms using de Rham homology and Poincare duality.

Explored the role of the intersection form in defining the constitutive law.

Discussed how electromagnetic structure influences wave motion.

Abstract

The axioms of topological electromagnetism are refined by the introduction of the de Rham homology of k-vector fields on orientable manifolds and the use of Poincare duality in place of Hodge duality. The central problem of defining the electromagnetic constitutive law is elaborated upon in the linear and nonlinear cases. The manner by which the spacetime metric might follow from the constitutive law is examined in the linear case. The possibility that the intersection form of the spacetime manifold might play a role in defining a topological basis for the constitutive law is explored. The manner by which wave motion might follow from the electromagnetic structure is also discussed.