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

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.

Contribution to the joint Proceedings of the XIX Mexican School of Particles and Fields and the XXXV Annual Meeting of the Division of Particles and Fields of the Mexican Society of Physics. 8 pages

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• Dynamical Casimir effect with screened scalar fields
• Renormalisation in maximally symmetric spaces and semiclassical gravity in Anti-de Sitter spacetime
• Spontaneous particle creation by oscillating compact stars