We review recent developments in the Casimir effect which arises in quantization volumes restricted by material boundaries and in spaces with non-Euclidean topology. The starting point of our discussion is the novel exact solution for the electromagnetic Casimir force in the configuration of a cylinder above a plate. The related work for the scalar Casimir effect in sphere-plate configuration i...

The phenomena implied by the existence of quantum vacuum fluctuations, grouped under the title of the Casimir effect, are reviewed, with emphasis on new results discovered in the past four years. The Casimir force between parallel plates is rederived as the strong-coupling limit of δ-function potential planes. The role of surface divergences is clarified. A summary of effects relevant to measur...

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...

This paper summarizes the contribution presented at the IX Marcel Grossmann Meeting (Rome, July 2000). A simple model of spacetime foam, made by N Schwarzschild wormholes in a semiclassical approximation, is here proposed. The Casimir-like energy of the quantum fluctuation of such a model and its probability of being realized are computed. Implications on the Bekenstein-Hawking entropy and the ...

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...

We provide a review of both new experimental and theoretical developments in the Casimir effect. The Casimir effect results from the alteration by the boundaries of the zero-point electromagnetic energy. Unique to the Casimir force is its strong dependence on shape, switching from attractive to repulsive as function of the size, geometry and topology of the boundary. Thus the Casimir force is a...

We apply general formalism of quantum field theory and addition theorem for Bessel functions to derive formula for the Casimir-Polder energy of interaction between a polarizable particle and a dilute dielectric ball and Casimir energy of a dilute dielectric ball. The correspondence between the Casimir-Polder formula and Casimir energy of a dilute dielectric ball is shown. Different approaches t...

We study the Casimir piston for massless scalar fields obeying Dirichlet boundary conditions in a three dimensional cavity with sides of arbitrary lengths a, b and c where a is the plate separation. We obtain an exact expression for the Casimir force on the piston valid for any values of the three lengths. As in the electromagnetic case with perfect conductor conditions, we find that the Casimi...

The analytic asymptotic expressions for the Casimir free energy, pressure and entropy at low temperature in the configuration of one metal and one dielectric plate are obtained. For this purpose we develop the perturbation theory in a small parameter proportional to the product of the separation between the plates and the temperature. This is done using both the simplified model of an ideal met...