Zero and finite temperature Casimir effect of massive vector field between real metals

TL;DR

This paper generalizes the Lifshitz formula to calculate the Casimir effect of a massive vector field between real metal slabs, analyzing its behavior at different temperatures, masses, and conductivities, with implications for Randall-Sundrum models.

Contribution

It introduces a generalized Lifshitz formula for massive vector fields and explores the Casimir effect under various physical limits for real metal slabs.

Findings

Casimir energy and force depend on temperature, mass, and conductivity.

Asymptotic behaviors are characterized in different physical regimes.

Application to Randall-Sundrum spacetime is discussed.

Abstract

We consider the Casimir effect of a massive vector field between two semi-infinite dielectric slabs. We first derive the generalization of the Lifshitz formula that gives the Casimir interaction energy of two magnetodielectric slabs separated by a magnetodielectric medium due to the vacuum fluctuations of a massive vector field. We then discuss the asymptotic behaviors of the Casimir energy and the Casimir force in various limits, such as low temperature, high temperature, small mass, large mass, up to the first order in the finite conductivity correction, for two real metal semispaces whose dielectric property is described by the plasma model. Application to the Casimir effect in Randall-Sundrum spacetime is briefly discussed.