A simple and direct time domain derivation of the dyadic Green's function for a uniformly moving non-dispersive dielectric-magnetic medium

The present contribution is concerned with deriving the relativistic electric and magnetic time-dependent dyadic Green's functions of an isotropic dielectric-magnetic medium (at the frame-at-rest) that is moving in a uniform relativistic velocity under the framework of the Minkowski constitutive relations. The results presented here correct previous reports in the literature [R. Compton, J. Math. Phys. 7, 2145 (1966)] and [C. Tai, J. Math. Phys. 8, 646 (1967)]. By applying a simple space-time and fields-sources transformation, scalarization of the vectorial problem is obtained. Thus the electromagnetic dyads are evaluated from the Green's function of the scalar (time-dependent) wave equation in free space. Emphasis is placed on a simple and direct time domain derivation.