Casimir effect from macroscopic quantum electrodynamics

TL;DR

This paper derives the Casimir effect using a rigorous macroscopic quantum electrodynamics framework, providing a consistent quantum treatment applicable to complex media and clarifying issues with traditional Lifshitz theory.

Contribution

It presents a novel derivation of the Casimir effect from a canonical quantization of macroscopic electromagnetism, valid for inhomogeneous dispersive media, and addresses limitations of previous approaches.

Findings

Derivation of Casimir energy density and stress tensor from quantum electrodynamics.

Results applicable to arbitrary inhomogeneous magnetodielectrics.

Clarification of the quantum nature of Casimir forces beyond Lifshitz theory.

Abstract

The canonical quantization of macroscopic electromagnetism was recently presented in New J. Phys. 12 (2010) 123008. This theory is here used to derive the Casimir effect, by considering the special case of thermal and zero-point fields. The stress-energy-momentum tensor of the canonical theory follows from Noether's theorem, and its electromagnetic part in thermal equilibrium gives the Casimir energy density and stress tensor. The results hold for arbitrary inhomogeneous magnetodielectrics and are obtained from a rigorous quantization of electromagnetism in dispersive, dissipative media. Continuing doubts about the status of the standard Lifshitz theory as a proper quantum treatment of Casimir forces do not apply to the derivation given here. Moreover, the correct expressions for the Casimir energy density and stress tensor inside media follow automatically from the simple restriction to thermal equilibrium, without the need for complicated thermodynamical or mechanical arguments.