Casimir effect for arbitrary materials: contributions within and beyond the light cone

Abstract

We obtain an expression for the Casimir force within a planar cavity without making particular models or assumptions about the nature of its walls. We obtain the energy and stress tensor in a closed ancillary system that has the same optical response as the target system, but that allows a fully quantum-mechanical treatment of the electromagnetic degrees of freedom. Our results constitute a generalization of the Lifshitz formula, applicable to a wide class of materials, which could be semi-infinite or finite, local or spatially dispersive, homogeneous or layered, dissipative or dissipationless. We discuss the incorporation of evanescent fields in the formalism, the electromagnetic normal modes of the system, its thermodynamic properties, and the generalization of our results to arbitrary geometries.