A heuristic way to calculate the approximate value of the Casimir force is introduced

We compute the influence of an external magnetic field on the Casimir energy of a massive charged scalar field confined between two parallel infinite plates. For this case the obtained result shows that the magnetic field inhibits the Casimir effect. The Casimir effect can be generally defined as the effect of a non-trivial space topology on the vacuum fluctuations of relativistic quantum field...

The Casimir effect in an inhomogeneous dielectric is investigated using Lifshitz’s theory of electromagnetic vacuum energy. A permittivity function that depends continuously on one Cartesian coordinate is chosen, bounded on each side by homogeneous dielectrics. The result for the Casimir stress is infinite everywhere inside the inhomogeneous region, a divergence that does not occur for piece-wi...

With the recent growth of nano physics, the Casimir effect has gained more attention, and this time also on the experimental side [2–6], because it is clear that Casimir forces will have to be taken into account where micro and nanostructures are involved [7,8]. These experiments were made between a sphere and a plate, a setup that has proved more easily applicable in experiments. Recently Ianu...

In this paper we examine Casimir effect in the case of tachyonic field, which is connected with particles with negative four-momentum square (m2 < 0). We consider here only the case of the one dimensional, scalar field. In order to describe tachyonic field, we use the absolute synchronization scheme preserving Lorentz invariance. The renormalized vacuum energy is calculated by means of the Abel...

In his autobiography Casimir barely mentioned the Casimir effect, but remarked that it is “of some theoretical significance” [1]. We will describe some aspects of Casimir effects that appear to be of particular significance now, more than half a century after Casimir’s famous paper [2].

We propose a new approach to the Casimir effect based on classical ray optics. We define and compute the contribution of classical optical paths to the Casimir force between rigid bodies. Our approach improves upon the proximity force approximation. It can be generalized easily to arbitrary geometries, different boundary conditions, to the computation of Casimir energy densities and to many oth...