The Casimir effect: some aspects

TL;DR

This paper reviews the historical development, computational methods, and experimental confirmation of the Casimir effect, including explicit calculations for different boundary conditions and related phenomena involving magnetic fields and vacuum properties.

Contribution

It compares global and local methods for calculating Casimir forces and provides explicit examples, enhancing understanding of the effect's theoretical and experimental aspects.

Findings

Explicit calculations of Casimir forces between parallel plates.

Discussion of Robin boundary conditions effects.

Comments on experimental confirmation of the Casimir effect.

Abstract

We start this paper with a historical survey of the Casimir effect, showing that its origin is related to experiments on colloidal chemistry. We present two methods of computing Casimir forces, namely: the global method introduced by Casimir, based on the idea of zero-point energy of the quantum electromagnetic field, and a local one, which requires the computation of the energy-momentum stress tensor of the corresponding field. As explicit examples, we calculate the (standard) Casimir forces between two parallel and perfectly conducting plates and discuss the more involved problem of a scalar field submitted to Robin boundary conditions at two parallel plates. A few comments are made about recent experiments that undoubtedly confirm the existence of this effect. Finally, we briefly discuss a few topics which are either elaborations of the Casimir effect or topics that are related in some way to this effect as, for example, the influence of a magnetic field on the Casimir effect of charged fields, magnetic properties of a confined vacuum and radiation reaction forces on non-relativistic moving boundaries.