A dispersion relation for the density of states with application to the Casimir effect

► The density of states is determined by the log determinant of the scattering matrix. ► But this “Krein Forluma” is divergent. ► We remove the divergence by using a dispersion relation. ► A formula for the Casimir energy in terms of the optical scattering matrix follows. ► No rotational symmetries are assumed, nor is perturbation theory used.