A short review of the Casimir effect with emphasis on dynamical boundary conditions

TL;DR

This paper reviews the static and dynamical Casimir effects, emphasizing the role of dynamical boundary conditions in experimental verification and discussing theoretical calculations of Casimir energies and forces.

Contribution

It provides a concise review of the Casimir effect with a focus on dynamical boundary conditions and discusses previous work on calculating Casimir energies and forces.

Findings

Experimental verification of the dynamical Casimir effect by Wilson et al.

Methodology for computing local and total Casimir energies.

Future directions for rigorous theoretical foundations of dynamical Casimir effect predictions.

Abstract

We give a short review on the static and dynamical Casimir effects, recalling their historical prediction, as well as their more recent experimental verification. We emphasise on the central role played by so-called {\it dynamical boundary conditions} (for which the boundary condition depends on a second time derivative of the field) in the experimental verification of the dynamical Casimir effect by Wilson et al. We then go on to review our previous work on the static Casimir effect with dynamical boundary conditions, providing an overview on how to compute the so-called local Casimir energy, the total Casimir energy and the Casimir force. We give as a future perspective the direction in which this work should be generalised to put the theoretical predictions of the dynamical Casimir effect experiments on a rigorous footing.