Casimir energy, dispersion, and the Lifshitz formula

TL;DR

This paper demonstrates that the standard dispersive electromagnetic energy form is essential for deriving the Lifshitz force between dielectric media, clarifying theoretical foundations and providing explicit derivations.

Contribution

It establishes the necessity of using the dispersive form of electromagnetic energy in Lifshitz force derivations and explicitly derives the formula from quantum vacuum energy considerations.

Findings

Dispersive energy form is required for Lifshitz force derivation

Explicit derivation of Lifshitz formula including dispersion

Addresses energy constancy and electrostrictive forces

Abstract

Despite suggestions to the contrary, we show in this paper that the usual dispersive form of the electromagnetic energy must be used to derive the Lifshitz force between parallel dielectric media. This conclusion follows from the general form of the quantum vacuum energy, which is the basis of the multiple-scattering formalism. As an illustration, we explicitly derive the Lifshitz formula for the interaction between parallel dielectric semispaces, including dispersion, starting from the expression for the total energy of the system. The issues of constancy of the energy between parallel plates and of the observability of electrostrictive forces are briefly addressed.