The Casimir energy in a dispersive and absorptive medium in the Fano diagonalization approach

We calculate the Casimir energy of the electromagnetic field in the one-dimensional space between two metallic plates filled with a dispersive and absorptive dielectric in the framework of a microscopic approach in which the medium is modeled by a set of oscillators with continuously distributed frequencies. We analyze the treatment of singular expressions used in other papers and show that with appropriate regularization and omission of certain infinite terms, the results coincide with those obtained in an approach without such singularities. We study the asymptotic behavior at large distances and conclude that it always corresponds to attraction, but the influence of the dielectric can lead to repulsion at finite distances.