A. A. Saharian

Casimir effect for scalar fields under Robin boundary conditions on plates

We study the Casimir effect for scalar fields with general curvature coupling subject to mixed boundary conditions (1 + βmnμ∂μ) = 0 at x = am on one (m = 1) and two (m = 1, 2) parallel plates at a distance a ≡ a2 − a1 from each other. Making use of the generalized Abel–Plana formula previously established by one of the authors [1], the Casimir energy densities are obtained as functions of β1 and of β1, β2, a respectively. In the case of two parallel plates, a decomposition of the total Casimir energy into volumic and superficial contributions is provided. The possibility of finding a vanishing energy for particular parameter choices is shown and the existence of a minimum to the surface part is also observed. We show that there is a region in the space of parameters defining the boundary conditions in which the Casimir forces are repulsive for small distances and attractive for large distances. This yields the interesting possibility of stabilizing the distance between the plates by using the vacuum forces.

The Casimir effect on background of conformally flat brane-world geometries

Abstract The Casimir effect due to conformally coupled bulk scalar fields on background of conformally flat brane-world geometries is investigated. In the general case of mixed boundary conditions formulae are derived for the vacuum expectation values of the energy–momentum tensor and vacuum forces acting on boundaries. The special case of the AdS bulk is considered and the application to the Randall–Sundrum scenario is discussed. The possibility for the radion stabilization by the vacuum forces is demonstrated.

Repulsive Casimir effect from extra dimensions and Robin boundary conditions: From branes to pistons

We evaluate the Casimir energy and force for a massive scalar field with general curvature coupling parameter, subject to Robin boundary conditions on two codimension-one parallel plates, located on a (

On the energy-momentum tensor for a scalar field on manifolds with boundaries

D+1

Wightman function and Casimir densities on AdS bulk with application to the Randall–Sundrum braneworld

)-dimensional background spacetime with an arbitrary internal space. The most general case of different Robin coefficients on the two separate plates is considered. With independence of the geometry of the internal space, the Casimir forces are seen to be attractive for special cases of Dirichlet or Neumann boundary conditions on both plates and repulsive for Dirichlet boundary conditions on one plate and Neumann boundary conditions on the other. For Robin boundary conditions, the Casimir forces can be either attractive or repulsive, depending on the Robin coefficients and the separation between the plates, what is actually remarkable and useful. Indeed, we demonstrate the existence of an equilibrium point for the interplate distance, which is stabilized due to the Casimir force, and show that stability is enhanced by the presence of the extra dimensions. Applications of these properties in braneworld models are discussed. Finally, the corresponding results are generalized to the geometry of a piston of arbitrary cross section.

Scalar Casimir effect for D-dimensional spherically symmetric Robin boundaries

We argue that already at the classical level the energy-momentum tensor for a scalar field on manifolds with boundaries in addition to the bulk part contains a contribution located on the boundary. Using the standard variational procedure for the action with the boundary term, the expression for the surface energy-momentum tensor is derived for arbitrary bulk and boundary geometries. Integral conservation laws are investigated. The corresponding conserved charges are constructed and their relation to the proper densities is discussed. Further, we study the vacuum expectation value of the energy-momentum tensor in the corresponding quantum field theory. It is shown that the surface term in the energy-momentum tensor is essential in obtaining the equality between the vacuum energy, evaluated as the sum of the zero-point energies for each normal mode of frequency, and the energy derived by the integration of the corresponding vacuum energy density. As an application, by using the zeta function technique, we evaluate the surface energy for a quantum scalar field confined inside a spherical shell.

Vacuum polarization induced by a cylindrical boundary in the cosmic string spacetime

Abstract Positive frequency Wightman function and vacuum expectation value of the energy–momentum tensor are computed for a massive scalar field with general curvature coupling parameter subject to Robin boundary conditions on two parallel plates located on ( D + 1 ) -dimensional AdS background. The general case of different Robin coefficients on separate plates is considered. The mode summation method is used with a combination of a variant of the generalized Abel–Plana formula for the series over zeros of combinations of cylinder functions. This allows us to extract manifestly the parts due to the AdS spacetime without boundaries and boundary induced parts. The asymptotic behavior of the vacuum densities near the plates and at large distances is investigated. The vacuum forces acting on the boundaries are presented as a sum of the self-action and interaction forces. The first one contains well-known surface divergences and needs further regularization. The interaction forces between the plates are attractive for Dirichlet scalar. We show that there is a region in the space of parameters defining the boundary conditions in which the interaction forces are repulsive for small distances and attractive for large distances. An application to the Randall–Sundrum braneworld with arbitrary mass terms on the branes is discussed.

Vacuum densities and zero-point energy for fields obeying Robin conditions on cylindrical surfaces

The vacuum expectation values for the energy-momentum tensor of a massive scalar field with general curvature coupling and obeying the Robin boundary condition on spherically symmetric boundaries in D-dimensional space are investigated. The expressions are derived for the regularized vacuum energy density and radial and azimuthal stress components (i) inside and outside a single spherical surface and (ii) in the intermediate region between two concentric spheres. A regularization procedure is carried out by making use of the generalized Abel-Plana formula for the series over zeros of cylinder functions. The asymptotic behavior of the vacuum densities near the sphere and at large distances is investigated. A decomposition of the Casimir energy into volumic and surface parts is provided for both cases (i) and (ii). We show that the mode sum energy, evaluated as a sum of the zero-point energy for each normal mode of frequency, and the volume integral of the energy density in general are different, and argue that this difference is due to the existence of an additional surface energy contribution.

Electromagnetic Casimir densities induced by a conducting cylindrical shell in the cosmic string spacetime

In this paper we investigate the Wightman function, the renormalized vacuum expectation values of the field square, and the energy-momentum tensor for a massive scalar field with general curvature coupling inside and outside of a cylindrical shell in the generalized spacetime of straight cosmic string. For the general case of Robin boundary condition, by using the generalized Abel-Plana formula, the vacuum expectation values are presented in the form of the sum of boundary-free and boundary-induced parts. The asymptotic behavior of the vacuum expectation values of the field square, energy density and stresses are investigated in various limiting cases. The generalization of the results to the exterior region is given for a general cylindrically symmetric static model of the string core with finite support.

Casimir energy–momentum tensor for a brane in de Sitter spacetime

The Casimir effect for general Robin conditions on the surface of a cylinder in