Related papers: Casimir energy in multiply connected static hyperb…
A few years ago, Cornish, Spergel and Starkman (CSS), suggested that a multiply connected ``small'' Universe could allow for classical chaotic mixing as a pre-inflationary homogenization process. The smaller the volume, the more important…
The Casimir effect in compact hyperbolic Universes was numerically obtained in previous publications. In this talk, I expose these results.
In this article, we obtain the explicit expression of the Casimir energy for 2-dimensional Clifford-Klein space forms in terms of the geometrical data of the underlying spacetime with the help of zeta-regularization techniques. The…
We derive a trace formula for the spectra of quantum mechanical systems in hyperbolic polygons which are the fundamental domains of discrete isometry groups acting in the two dimensional hyperboloid. Using this trace formula and the point…
The original Casimir effect results from the difference in the vacuum energies of the electromagnetic field, between that in a region of space with boundary conditions and that in the same region without boundary conditions. In this paper…
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…
We discuss the role Casimir energies may play in addressing issues of moduli stabilization and dark energy. In particular, we examine a (non-supersymmetric) brane world scenario with toroidal extra dimensions in which Casimir energies of…
The contribution of elliptic fixed points to the scalar Casimir energy on compact quotients of the upper half hyperbolic plane is computed for a propagation operator conformal in three dimensions. The expression involves derivatives of…
The contribution, E, of hyperbolic elements to the scalar Casimir energy on a compact quotient of the upper half hyperbolic plane is computed for a propagation operator conformal in three dimensions. Due to the proliferation of prime closed…
Casimir energies on space-times having general lens spaces as their spatial sections are shown to be given in terms of generalised Dedekind sums related to Zagier's. These are evaluated explicitly in certain cases as functions of the order…
The Casimir energy for a massless, neutral scalar field in presence of a point interaction is analyzed using a general zeta-regularization approach developed in earlier works. In addition to a regular bulk contribution, there arises an…
Recently many people have discussed the possibility that the universe is hyperbolic and was in an inflationary phase in the early stage. Under these assumptions, it is shown that the universe cannot have compact hyperbolic time-slices.…
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…
We develop an exact method for computing the Casimir energy between arbitrary compact objects, both with boundary conditions for a scalar field and dielectrics or perfect conductors for the electromagnetic field. The energy is obtained as…
We review different computation methods for the renormalised energy momentum tensor of a quantised scalar field in an Einstein Static Universe. For the extensively studied conformally coupled case we check their equivalence; for different…
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…
A review of positive energy theorems for asymptotically hyperbolic manifolds
The Casimir energy is constructed for a system consisting of two semi-infinite slabs of anisotropic material. Each of them is characterized by bulk complex dielectric permittivity tensor and surface conductivity on the free boundary. We…
We discuss a numerical relation between the cosmological constant and the vacuum energy arising from the Casimir effect in extra dimensions
We develop an exact method for computing the Casimir energy between arbitrary compact objects, either dielectrics or perfect conductors. The energy is obtained as an interaction between multipoles, generated by quantum current fluctuations.…