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 Casimir force due to thermal fluctuations (or pseudo-Casimir force) was recently calculated for the perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to quantum fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC) confined to a parallel plate geometry was also recently calculated for Dirichlet boundary conditions. In this p...

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...

We apply general formalism to derive Casimir surface force on a dilute dielectric ball without divergencies in intermediate calculations. The correspondence between the Casimir-Polder formula and Casimir surface force is shown. PACS numbers: 03.70.+k, 11.10.Gh, 12.20.-m, 12.20.Ds, 42.50.Lc E-mail: [email protected]

A 3D finite-element numerical simulation was developed to investigate Casimir forces in arbitrary geometries. The code was verified comparing it with results obtained from analytical equations. Appling the simulation to previously not assessed configurations, new Casimir properties were found such as repulsive Casimir forces in groove like structures.

Casimir W-algebras are shown to be exist in such a way that the conformal spins of primary (generating) fields coincide with the orders of independent Casimir operators. We show here that this coincidence can be extended further to the case that these generating fields have the same eigenvalues with the Casimir operators.

The zero-point quantum fluctuations of the electromagnetic field in vacuum are known to give rise to a long-range attractive force between metal plates (Casimir effect). For ferromagnetic layers separated by vacuum, it is shown that the interplay of the Casimir effect and of the magneto-optical Kerr effect gives rise to a long-range magnetic interaction. The Casimir magnetic force is found to d...

In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero point energies of quantum fields are “real”. On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) betwee...