Inertial forces in the Casimir effect with two moving plates

TL;DR

This paper derives the dynamical Casimir force for two parallel plates moving normally in D-dimensional space using linear response theory and dimensional regularization, revealing finite mass corrections related to the static Casimir energy.

Contribution

It introduces a method combining linear response theory and dimensional regularization to analyze the dynamical Casimir effect with moving plates in arbitrary dimensions.

Findings

Finite, separation-dependent mass corrections are derived.

Mass correction is proportional to the static Casimir energy.

Results align with Einstein's mass-energy equivalence law.

Abstract

We combine linear response theory and dimensional regularization in order to derive the dynamical Casimir force in the low frequency regime. We consider two parallel plates moving along the normal direction in $D-$dimensional space. We assume the free-space values for the mass of each plate to be known, and obtain finite, separation-dependent mass corrections resulting from the combined effect of the two plates. The global mass correction is proportional to the static Casimir energy, in agreement with Einstein's law of equivalence between mass and energy for stressed rigid bodies.