The ground state energy of the massive scalar field with non-conformal coupling $\xi$ on the short-throat flat-space wormhole background is calculated by using zeta renormalization approach. We discuss the renormalization and relevant heat kernel coefficients in detail. We show that the stable configuration of wormholes can exist for $\xi > 0.123$. In particular case of massive conformal scalar field with $\xi=1/6$, the radius of throat of stable wormhole $a\approx 0.16/m$. The self-consistent wormhole has radius of throat $a\approx 0.0141 l_p $ and mass of scalar boson $m\approx 11.35 m_p$ ($l_p$ and $m_p$ are the Planck length and mass, respectively).Comment: revtex, 18 pages, 3 eps figures. accepted in Phys.Rev.

We consider the vacuum energy of the electromagnetic field interacting with a spherical plasma shell together with a model for the classical motion of the shell. We calculate the heat kernel coefficients, especially that for the TM mode, and carry out the renormalization by redefining the parameters of the classical model. It turns out that this is possible and results in a model, which in the limit of the plasma shell becoming an ideal conductor reproduces the vacuum energy found by Boyer in 1968.

We consider the self-energy and the self-force for an electrically charged particle at rest in the wormhole space-time. We develop a general approach to finding the self-force and apply it to the two specific profiles of the wormhole throat with singular and with smooth curvature. The self-force for these two profiles is found in manifest form; it turns out to be an attractive force. We also find an expression for the self-force in the case of arbitrary symmetric throat profile. Far from the throat the self-force is always attractive.

We found the contribution to the vacuum expectation value of the energy-momentum tensor of a massive Dirac field due to the conical geometry of the cosmic string space-time. The heat kernel and heat kernel expansion for the squared Dirac operator in this background are also considered and the first three coefficients were found in an explicity form.

The Casimir-Polder interaction between an atom and a multilayered system composed of infinitely thin planes is considered using the zeta-function regularization approach with zero-point energies summation. As a prototype material, each plane is represented by a graphene sheet, an atomically thin layer of Carbon atoms organized in a hexagonal lattice, whose optical response is described by a constant conductivity or Drude-Lorentz model conductivity. Asymptotic expressions for various separations are derived and compared to numerical calculations. We distinguish between large atom/plane distance limit, where retardation effects are prominent, and small atom/plane distance limit, where the typical van der Waals coefficient is found to be dependent on the number of graphenes and characteristic separations. The calculated energies for different atoms and graphene conductivity models brings forward the basic science of the Casimir-Polder effect and suggests ways to manipulate this interaction experimentally.

We calculate the renormalized vacuum average of the energy-momentum tensor of massless lefthanded spinor field in the pointlike global monopole spacetime using point-separation approach. The general structure of the vacuum average of the energy-momentum tensor is obtained and expressed in terms of < T 0 0 > ren component, explicit form of which is analyzed in great details for arbitrary solid angle deficit. 98.80.Cq, 14.80.Hv, 95.30.S

We consider the self-energy and the self-force for scalar massive and massless particles at rest in the wormhole space-time. We develop a general approach to obtain the self-force and apply it to the two specific profiles of the wormhole throat, namely, with singular and with smooth curvature. We found that the self-force changes its sign at the point where nonminimal coupling $\xi = 1/8$ (for massless case) and it tends to infinity for specific values of $\xi$. It may be attractive as well repulsive depending on the profile of the throat. For massless particle and minimal coupling case the electromagnetic results are recovered.Comment: 15 pages, 2 figure

We calculate the ground state energy of a massive scalar field in the background of a cosmic string of finite thickness ͑Gott-Hiscock metric͒. Using zeta functional regularization we discuss the renormalization and the relevant heat kernel coefficients in detail. The finite ͑nonlocal͒ part of the ground state energy is calculated in 2ϩ1 dimensions in the approximation of a small mass density of the string. By a numerical calculation it is shown to vanish as a function of the radius of the string and of the parameter of the nonconformal coupling.