  In this article, we put forward a new approach to electrodynamics of
materials. Based on the identification of induced electromagnetic fields as the
microscopic counterparts of polarization and magnetization, we systematically
employ the mutual functional dependencies of induced, external and total field
quantities. This allows for a unified, relativistic description of the
electromagnetic response without assuming the material to be composed of
electric or magnetic dipoles. Using this approach, we derive universal
(material-independent) relations between electromagnetic response functions
such as the dielectric tensor, the magnetic susceptibility and the microscopic
conductivity tensor. Our formulae can be reduced to well-known identities in
special cases, but more generally include the effects of inhomogeneity,
anisotropy, magnetoelectric coupling and relativistic retardation. If combined
with the Kubo formalism, they would also lend themselves to the ab initio
calculation of all linear electromagnetic response functions.
