Alternative formulation of the macroscopic field equations in a linear magneto-dielectric medium: Field equations

TL;DR

This paper presents an alternative formulation of macroscopic electromagnetic field equations in linear magneto-dielectric media, where material properties are incorporated through coordinate renormalization, offering new perspectives on physical and boundary condition issues.

Contribution

It introduces a novel formulation of macroscopic field equations that embeds material properties into coordinate transformations, expanding the theoretical framework of continuum electrodynamics.

Findings

Reformulation as an identity of Maxwell--Minkowski equations

Material properties incorporated via coordinate renormalization

Raises new questions on relativity and boundary conditions

Abstract

We derive an alternative formulation of the field equations for macroscopic electromagnetic fields in a linear magneto-dielectric medium as an identity of the Maxwell--Minkowski equations, complementing a variety of other representations including the Amp\`ere, Chu, Lorentz, and Minkowski formulations of continuum electrodynamics. In the new formulation of the macroscopic field equations, the material properties are carried as a renormalization of the temporal and spatial coordinates instead of as independent material constants. The new representation of the field equations raises some interesting physical issues with relativity and boundary conditions.