Functional approach to electrodynamics of media

• Electrodynamics of materials is derived from first principles.
• Induced electromagnetic fields regarded as functionals of external perturbations.
• Four universal relations hold between electromagnetic response functions.
• 36-component constitutive tensor reduced to 9-component current response tensor.
• General formulae for magnetoelectric couplings suitable for ab initio calculations.

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.