Related papers: Casimir effect for scalar field rotating on a disk
The survey summarizes briefly the results obtained recently in the Casimir effect studies considering the following subjects: i) account of the material characteristics of the media and their influence on the vacuum energy (for example,…
In the study of quantum vacuum energy and the Casimir effect, it is desirable to model the conductor by a potential of the form $V(z)=z^\alpha$. This "soft wall" model was proposed so as to avoid the violation of the principle of virtual…
The survey summarizes briefly the results obtained recently in the Casimir effect studies considering the following subjects: i) account of the material characteristics of the media and their influence on the vacuum energy (for example,…
We calculate the \hkks for the \elm field in the background of a dielectric cylinder with non equal speeds of light inside and outside. The coefficient $a_{2}$ whose vanishing makes the vacuum energy of a massless field unique, turns out to…
We study the vacuum interaction of a scalar field and two concentric spheres defined by a singular potential on their surfaces. The potential is a linear combination of the Dirac-$\delta$ and its derivative. The presence of the delta prime…
In the $(\epsilon_1-\epsilon_2)^2$--approximation the Casimir energy of a dilute dielectric ball is derived using a simple and clear method of the mode summation. The addition theorem for the Bessel functions enables one to present in a…
The Casimir force on a $D$-dimensional sphere due to the confinement of a massless scalar field is computed as a function of $D$, where $D$ is a continuous variable that ranges from $-\infty$ to $\infty$. The dependence of the force on the…
The resonant scalar particle generation for a swinging cavity resonator in the Casimir vacuum is examined. It is shown that the number of particles grows exponentially when the cavity rotates at some specific external frequency.
The Casimir energy for massless scalar field of two parallel conductor, in two dimensional Schwarzchild black hole background, with Dirichlet boundary conditions is calculated by making use of general properties of renormalized stress…
In this work we analyze the spectral zeta function for massless scalar fields propagating in a $D$-dimensional flat space under the influence of a shell potential. The shell potential is defined in terms of the two-interval self-adjoint…
We study the field theoretical model of a real scalar field in presence of spacial inhomogeneity in form of a finite width mirror (material layer). The interaction of the scalar field with the defect is described with position-dependent…
In this study, the Casimir energy for massive scalar field with periodic boundary condition was calculated on spherical surfaces with $S^1$, $S^2$ and $S^3$ topologies. To obtain the Casimir energy on spherical surface, the contribution of…
It has been demonstrated, using variational methods, that quantum vacuum energy gravitates according to the equivalence principle, at least for the finite Casimir energies associated with perfectly conducting parallel plates. This…
Wightman function, the vacuum expectation values of the field square and the energy-momentum tensor are investigated for a massive scalar field with general curvature coupling parameter in the region between two coaxial cylindrical…
We compute the first radiative correction to the Casimir energy of a massive scalar field with a quartic self-interaction in the presence of two parallel plates. Three kinds of boundary conditions are considered: Dirichlet-Dirichlet,…
We consider a massless scalar field in 1+1 dimensions that satisfies a Robin boundary condition at a non-relativistic moving boundary. Using the perturbative approach introduced by Ford and Vilenkin, we compute the total force on the moving…
This is the first one of a series of papers about zeta regularization of the divergences appearing in the vacuum expectation value (VEV) of several local and global observables in quantum field theory. More precisely we consider a…
The Casimir effect is a macroscopic evidence of the quantum nature of the vacuum. On a ring, it leads to a finite size correction to the vacuum energy. In this work, we show that this vacuum's energy and pressure acquire additional, sizable…
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…
Applying the general framework for local zeta regularization proposed in Part I of this series of papers, we compute the renormalized vacuum expectation value of several observables (in particular, of the stress-energy tensor and of the…