Related papers: Vacuum energy in conical space with additional bou…
We discuss the vacuum energy of a quantized scalar field in the presence of classical surfaces, defining bounded domains $\Omega \subset {\mathbb{R}}^{d}$, where the field satisfies ideal or non-ideal boundary conditions. For the…
Values for the vacuum energy of scalar fields under Dirichlet and Neuman boundary conditions on an infinite clylindrical surface are found, and they happen to be of opposite signs. In contrast with classical works, a complete zeta function…
The Casimir energy of a semi-circular cylindrical shell is calculated by making use of the zeta function technique. This shell is obtained by crossing an infinite circular cylindrical shell by a plane passing through the symmetry axes of…
The vacuum expectation values of the field squared and the energy-momentum tensor are investigated for a scalar field with Dirichlet boundary conditions and for the electromagnetic field inside a wedge with a coaxial cylindrical boundary.…
The response of vacuum to the presence of external conditions is the subject of this work. We consider a generalization of the Casimir effect in the presence of curved boundaries on which a sharp potential is concentrated. The profile of…
Vacuum expectation values of the field square and the energy-momentum tensor for the electromagnetic field are investigated for the geometry of a wedge with a coaxal cylindrical boundary. All boundaries are assumed to be perfectly…
The Casimir energy is evaluated for massless scalar fields under Dirichlet or Neumann boundary conditions, and for the electromagnetic field with perfect conductor boundary conditions on one and two infinite parallel plates moving by…
A simple method is proposed to construct the spectral zeta functions required for calculating the electromagnetic vacuum energy with boundary conditions given on a sphere or on an infinite cylinder. When calculating the Casimir energy in…
We study the Casimir energy of a minimally coupled, real, massless scalar field outside a spherically symmetric background potential. We obtain a general expression for the null energy condition in d dimensions and explicit expressions for…
We consider the vacuum energy for a scalar field subject to a frequency dependent boundary condition. The effect of a frequency cut-off is described in terms of an {\it incomplete} $\zeta$-function. The use of the Debye asymptotic expansion…
The vacuum energy density (Casimir energy) corresponding to a massless scalar quantum field living in different universes (mainly no-boundary ones), in several dimensions, is calculated. Hawking's zeta function regularization procedure…
We consider the vacuum energy of the electromagnetic field in systems characterized by a constant conductivity using the zeta-regularization approach. The interaction in two cases is investigated: two infinitely thin parallel sheets and an…
The Casimir effect for general Robin conditions on the surface of a cylinder in $D$-spacetime dimensions is studied for massive scalar field with general curvature coupling. The energy distribution and vacuum stress are investigated. We…
Quantum vacuum energy (Casimir energy) is reviewed for a mathematical audience as a topic in spectral theory. Then some one-dimensional systems are solved exactly, in terms of closed classical paths and periodic orbits. The relations among…
The vacuum energy density of electromagnetic field inside a perfectly conducting wedge is calculated by making use of the local zeta function technique. This regularization completely eliminates divergent expressions in the course of…
We calculate the vacuum (Casimir) energy for a scalar field with $\phi^4$ self-interaction in (1+1) dimensions non perturbatively, i.e., in all orders of the self-interaction. We consider massive and massless fields in a finite box with…
A general calculation of Casimir energies --in an arbitrary number of dimensions-- for massless quantized fields in spherically symmetric cavities is carried out. All the most common situations, including scalar and spinor fields, the…
We obtain new expressions for the Casimir energy between plates that are mimicked by the most general possible boundary conditions allowed by the principles of quantum field theory. This result enables to provide the quantum vacuum energy…
The effective one-loop potential on $R^{m+1}\times S^N$ spaces for massless tensor fields is evaluated. The Casimir energy is given as a value of $\zeta-$ function by means of which regularization is made. In even- dimensional spaces the…
We use a functional approach to the Casimir effect in order to evaluate the exact vacuum energy for a real scalar field in $d+1$ dimensions, in the presence of backgrounds that, in a particular limit, impose Dirichlet boundary conditions on…