On linear electromagnetic constitutive laws that define almost-complex structures

TL;DR

This paper investigates which linear electromagnetic constitutive laws induce almost-complex structures on the bundle of 2-forms in spacetime, revealing that only a restricted class, including isotropic and some bi-isotropic laws, have this property.

Contribution

It identifies the specific class of linear electromagnetic laws that define almost-complex structures, impacting the reduction to metric electromagnetism and wave propagation analysis.

Findings

Not all linear constitutive laws induce almost-complex structures.

Only a restricted class, including isotropic and some bi-isotropic laws, do so.

This influences the reduction to metric electromagnetism and wave behavior.

Abstract

It is shown that not all linear electromagnetic constitutive laws will define almost-complex structure on the bundle of 2-forms on the spacetime manifold when composed with the Poincare duality isomorphism, but only a restricted class of them that includes linear spatially isotropic and some bi-isotropic laws. Although this does not trivialize the formulation of the basic equations equations of pre-metric electromagnetism, it does affect their reduction to metric electromagnetism by its effect on the types of media that are reducible, and possibly its effect on the way that such media support the propagation of electromagnetic waves.