13 research outputs found

### Semiclassical wormholes

Smooth-throat wormholes are treated on as possessing quantum fluctuation
energy with scalar massive field as its source. Heat kernel coefficients of the
Laplace operator are calculated in background of the arbitrary-profile throat
wormhole with the help of the zeta-function approach. Two specific profile are
considered. Some arguments are given that the wormholes may exist. It serves as
a solution of semiclassical Einstein equations in the range of specific values
of length and certain radius of wormhole's throat and constant of non-minimal
connection.Comment: 28 pages, 4 figures, revtex

### Van der Waals interaction between an atom with spherical plasma shell

We consider the van der Waals energy of an atom near the infinitely thin
sphere with finite conductivity which model the fullerene. We put the sphere
into spherical cavity inside the infinite dielectric media, then calculate the
energy of vacuum fluctuations in framework of the zeta-function approach. The
energy for a single atom is obtained from this expression by consideration of
the rare media. In the limit of the infinite radius of the sphere the
Casimir-Polder expression for an atom and plate is recovered. For finite radius
of sphere the energy of an atom monotonously falls down as $d^{-3}$ close to
the sphere and $d^{-7}$ far from the sphere. For hydrogen atom on the surface
of the fullerene $C_{60}$ we obtain that the energy is $3.8 eV$. We obtain also
that the polarizability of fullerene is merely cube of its radius.Comment: 10 pages, 5 figure

### Self-force of a point charge in the space-time of a symmetric wormhole

We consider the self-energy and the self-force for an electrically charged
particle at rest in the wormhole space-time. We develop general approach and
apply it to 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 is 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.Comment: 18 pages, 3 figures Comments: corrected pdf, enlarged pape

### Zeta-function approach to Casimir energy with singular potentials

In the framework of zeta-function approach the Casimir energy for three
simple model system: single delta potential, step function potential and three
delta potentials is analyzed. It is shown that the energy contains
contributions which are peculiar to the potentials. It is suggested to
renormalize the energy using the condition that the energy of infinitely
separated potentials is zero which corresponds to subtraction all terms of
asymptotic expansion of zeta-function. The energy obtained in this way obeys
all physically reasonable conditions. It is finite in the Dirichlet limit and
it may be attractive or repulsive depending on the strength of potential. The
effective action is calculated and it is shown that the surface contribution
appears. The renormalization of the effective action is discussed.Comment: 17 pages, 2 figures, added reference, address correcte

### Casimir effect in a wormhole spacetime

We consider the Casimir effect for quantized massive scalar field with
non-conformal coupling $\xi$ in a spacetime of wormhole whose throat is rounded
by a spherical shell. In the framework of zeta-regularization approach we
calculate a zero point energy of scalar field. We found that depending on
values of coupling $\xi$, a mass of field $m$, and/or the throat's radius $a$
the Casimir force may be both attractive and repulsive, and even equals to
zero.Comment: 2 figures, 10 pages, added 2 reference

### Ground state energy in a wormhole space-time

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.

### Self-force of a point charge in the space-time of a massive wormhole

We consider the self-potential and the self-force for an electrically charged
particle at rest in the massive wormhole space-time. We develop general
approach for the renormalization of electromagnetic field of such particle in
the static space-times and apply it to the space-time of the wormhole with
parameter of the mass, $m$. The self-force is found in manifest form; it is an
attractive force. We discus the peculiarities due to massive parameter of the
wormhole.Comment: 10 pages, 1 figure text correcte

### Vacuum Expectation Value of the Spinor Massive field in the Cosmic String Space-Time

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.Comment: 9 pages, 1 figure (2 ref added) (enlarged version