The origin dependence of the material constants: the permittivity and the inverse permeability

Abstract

New derivations of origin-independent expressions for the electric permittivity are presented, starting either from the response function of the current density that defines the absorption coefficient, or from the off-resonance single-photon scattering amplitude that leads to the Kramers–Heisenberg dispersion formula. The resulting expression for the permittivity is compared with earlier work on the origin dependence of the material constants. Different origin-independent expressions for the permittivity, the inverse permeability and the magnetizability are calculated and discussed. By considering electromagnetic plane waves in the absence of external sources, the macroscopic Maxwell equations are used to describe the response of matter to external fields. In combination with the constitutive relations, a wave equation expressed in terms of the material constants is derived. It is shown that the different definitions of the material constants lead to the same wave equation. The non-uniqueness of the definitions of the material constants is discussed in this context. Finally, based on the discussions, we propose a possible unique, origin-independent definition of the material constants.