First-principle theory of the Casimir screening effect

TL;DR

This paper develops a first-principles quantum field theory approach to analyze how ionic fluctuations influence the Casimir force between conductive surfaces, emphasizing the importance of zero-frequency electromagnetic contributions.

Contribution

It introduces a formalism that separates ionic and electromagnetic fluctuations in the Casimir effect, highlighting the significance of zero Matsubara frequency components in the electromagnetic contribution.

Findings

Ionic fluctuations contribute separately from electromagnetic fluctuations.

The zero Matsubara frequency component is crucial for accurate Casimir force calculations.

The approach aligns with the separation hypothesis and differs from Lifshitz theory methods.

Abstract

In this paper, we use the formalism of finite-temperature quantum field theory to investigate the Casimir force between flat, ideally conductive surfaces containing confined, but mobile ions. We demonstrate that, in the Gaussian approximation, the ionic fluctuations contribute separately from the electromagnetic fluctuations that are responsible for the standard Casimir effect. This is in line with the "separation hypothesis", has been previously applied on a purely intuitive basis. Our analysis demonstrates the significance of calculating the zero Matsubara frequency component in the electromagnetic contribution, using the formula developed by Schwinger et al., as opposed to the approach based on Lifshitz theory used by other researchers.