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We derive an alternative formulation of the field equations for macroscopicelectromagnetic fields in a linear magneto-dielectric medium as an identity ofthe Maxwell--Minkowski equations, complementing a variety of otherrepresentations including the Amp\`ere, Chu, Lorentz, and Minkowskiformulations of continuum electrodynamics. In the new formulation of themacroscopic field equations, the material properties are carried as arenormalization of the temporal and spatial coordinates instead of asindependent material constants. The new representation of the field equationsraises some interesting physical issues with relativity and boundaryconditions.

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