Covariant Response Theory and the Boost Transform of the Dielectric Tensor

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.