After a short critique of the Minkowski formulae for the electromagnetic
constitutive laws in moving media, we argue that in actual fact the problem of
Lorentz-covariant electromagnetic response theory is automatically solved
within the framework of modern microscopic electrodynamics of materials. As an
illustration, we first rederive the well-known relativistic transformation
behavior of the microscopic conductivity tensor. Thereafter, we deduce from
first principles the transformation law of the wavevector- and
frequency-dependent dielectric tensor under Lorentz boost transformations.Comment: consistent with published version in Int. J. Mod. Phys. D (2017
