On linear electromagnetic constitutive laws that define almost-complex structures



It is shown that not all linear electromagnetic constitutive laws will define almost-complex structures on the bundle of 2-forms on the spacetime manifold when composed with the Poincaré duality isomorphism, but only a restricted class of them that includes linear spatially isotropic and some bi-isotropic constitutive laws. Although this result does not trivialize the formulation of the basic 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.