Functional approach to electrodynamics of media

Abstract

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.

Covariant response theory and the boost transform of the dielectric tensor

“…We note in passing that this assumption is completely in accord with the Fundamental Field Identifications introduced by the Functional Approach to electrodynamics of media [24][25][26][27][28]. By putting these transformation formulae into Eqs.…”

“…[13][14][15][16] for introductions) automatically come back into the focus. In this context, it is noteworthy that the ab initio calculation of electromagnetic response functions (for classical articles see [17][18][19][20], and for modern textbooks see [21][22][23]) relies on a microscopic approach to electrodynamics of media [24,25], according to which linear electromagnetic response properties are not given by shear constants (as it had traditionally been assumed) but by response functions constituting entire non-local integral kernels. This fact-which renders the historical derivation of the Minkowski formulae inapplicable-completely eluded researchers at the time when these had originally been developed, and hence the ensuing relativistic constitutive equations require a thorough re-investigation from the modern microscopic point of view.…”

Linear electromagnetic wave equations in materials

“…(2.62) as Finally, total functional derivatives with respect to electric and magnetic fields have already been defined in Ref. [27] as…”

“…[27], it is shown systematically that all standard relations between electromagnetic response functions can be recovered from the Universal Response Relations in suitable limiting cases. We conclude, in particular, that all physical response functions can be calculated explicitly in terms of the conductivity tensor.…”

“…For this purpose, we rely on a microscopic approach to electrodynamics of media, which is well-established in first-principles materials science and in plasma physics (see [19][20][21][22][23][24][25][26] for modern textbooks), and which is axiomatized by the Functional Approach to electrodynamics of media (see Refs. [18,[27][28][29][30][31][32]). …”