Classical electrodynamics with nonlocal constitutive equations

It is assumed that the coupling of the field quantities D^μv (x) and F _αβ (x) is nonlocal. This hypothesis leads to a theory of an electromagnetic field that has the following properties.(1) The source of the field F _αβ (x) exhibits a center of charge and a center of mass that do not coincide, in general.(2) The field componentF _0i=?c²E_i is regular at the origin.(3) In the first-order approximation the new field equations are equivalent to the conventional Maxwell field equations.(4) The conventional cutoff procedure in momentum space as practiced in the Maxwell-Lorentz theory is equivalent to the first-order approximation in terms of an invariant length ξ².(5) The gyromagnetic ratio of the source of F _αβ (x) is equal toc/mc for a quantum of chargee and massm.