Photon Green's function and Casimir energy in a medium - art. no. 045001

A new expansion is established for the Green's function of the electromagne tic field in a medium with arbitrary epsilon and mu. The obtained Born seri es is shown to consist of two types of terms: the usual terms (denoted P) t hat appear in the Lifshitz theory and a new kind of term (which we denote b y Q) associated with the changes in the permeability of the medium. Within this framework the case of a uniform velocity of light (epsilon mu =const) is studied. We obtain expressions for the Casimir energy density and the fi rst nonvanishing contribution is brought to a simplified form. For (arbitra ry) spherically symmetric mu, we obtain a simple expression for the electro magnetic energy density, and as an example we obtain from it the Casimir en ergy of a dielectric-diamagnetic ball. The technique presented can be appli ed to a variety of problems without recourse to eigenmode expansion and wit hout boundary condition considerations.