Related papers: Casimir energy of hyperbolic elements
For certain class of triangles (with angles proportional to $\fr{\pi}{N}$, $N\geq 3$) we formulate image method by making use of the group $G_N$ generated by reflections with respect to the three lines which form the triangle under…
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…
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 calculate the increase in the number of modes (the Kac number) per unit length and the change in the zero-point energy (the Casimir energy) of the electromagnetic field resulting from the introduction of a thin perfectly conducting…
The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically for the first time for an arbitrary physically possible frequency dispersion of dielectric permittivity $\epsilon(i\omega)$.…
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 study the supersymmetric Casimir energy $E_\mathrm{susy}$ of $\mathcal{N}=1$ field theories with an R-symmetry, defined on rigid supersymmetric backgrounds $S^1\times M_3$, using a Hamiltonian formalism. These backgrounds admit an…
The Casimir energy is computed in the geometry of interest for the most precise experiments, a plane and a sphere in electromagnetic vacuum. The scattering formula is developed on adapted plane-waves and multipole basis, leading to an…
Using recently developed techniques based on scattering theory, we find the electromagnetic Casimir energy for geometries involving semi-infinite planes, a case that is of particular interest in the design of microelectromechanical devices.…
We derive the electromagnetic self-energy and the radiative correction to the gyromagnetic ratio of a free electron using a Casimir energy approach. This method provides an attractive and straightforward physical basis for 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…
Casimir energy is calculated in the 5D warped system. It is compared with the flat one. The position/ momentum propagator is exploited. A new regularization, called {\it sphere lattice regularization}, is introduced. It is a direct…
The Casimir energy of a dilute homogeneous nonmagnetic dielectric ball at zero temperature is derived analytically within a microscopic realistic model of dielectrics for an arbitrary physically possible frequency dispersion of dielectric…
The Casimir energy is calculated in one-, two-, and three-dimensional spaces for the field with generalized coordinates and momenta satisfying the deformed Poisson brackets leading to the minimal length.
We compute the Casimir energy which arises in a bi-dimensional surface due to the quantum fluctuations of a scalar field. We assume that the boundaries are irregular and the field obeys Dirichlet condition. We re-parametrize the problem to…
We conjecture that for superconformal field theories in even dimensions, the supersymmetric Casimir energy on a space with topology $S^1\times S^{D-1}$ is equal to an equivariant integral of the anomaly polynomial. The equivariant…
A new formula for the Casimir energy of a dispersive dilute dielectric ball is discussed. The formula for the Casimir energy of a polarizable particle situated in a perfectly conducting wedge-shaped cavity is derived by a path-integral…
The Casimir energy corresponding to a massive scalar field with Dirichlet boundary conditions on a spherical bag is obtained. The field is considered, separately, inside and outside the bag. The renormalization procedure that is necessary…
Eigenmodes of electromagnetic field with perfectly conducting or infinitely permeable conditions on the boundary of a D-dimensional spherically symmetric cavity is derived explicitly. It is shown that there are (D-2) polarizations for TE…
Compact formulas are obtained for the Casimir energy of a relativistic perfect fluid confined to a $D$-dimensional hypercube with von Neumann or Dirichlet boundary conditions. The formulas are conveniently expressed as a finite sum of the…