9 research outputs found

### Evaluation of the Casimir Force for a Dielectric-diamagnetic Cylinder with Light Velocity Conservation Condition and the Analogue of Sellmeir's Dispersion Law

We study the Casimir pressure for a dielectric-diamagnetic cylinder subject
to light velocity conservation and with a dispersion law analogous to
Sellmeir's rule. Similarities to and differences from the spherical case are
pointed out.Comment: 19 pages Latex, no figures; discussion expanded. To appear in Physica
Script

### Electromagnetic Casimir densities for a wedge with a coaxial cylindrical shell

Vacuum expectation values of the field square and the energy-momentum tensor
for the electromagnetic field are investigated for the geometry of a wedge with
a coaxal cylindrical boundary. All boundaries are assumed to be perfectly
conducting and both regions inside and outside the shell are considered. By
using the generalized Abel-Plana formula, the vacuum expectation values are
presented in the form of the sum of two terms. The first one corresponds to the
geometry of the wedge without the cylindrical shell and the second term is
induced by the presence of the shell. The vacuum energy density induced by the
shell is negative for the interior region and is positive for the exterior
region. The asymptotic behavior of the vacuum expectation values are
investigated in various limiting cases. It is shown that the vacuum forces
acting on the wedge sides due to the presence of the cylindrical boundary are
always attractive.Comment: 21 pages, 7 figure

### Calculating Casimir Energies in Renormalizable Quantum Field Theory

Quantum vacuum energy has been known to have observable consequences since
1948 when Casimir calculated the force of attraction between parallel uncharged
plates, a phenomenon confirmed experimentally with ever increasing precision.
Casimir himself suggested that a similar attractive self-stress existed for a
conducting spherical shell, but Boyer obtained a repulsive stress. Other
geometries and higher dimensions have been considered over the years. Local
effects, and divergences associated with surfaces and edges have been studied
by several authors. Quite recently, Graham et al. have re-examined such
calculations, using conventional techniques of perturbative quantum field
theory to remove divergences, and have suggested that previous self-stress
results may be suspect. Here we show that the examples considered in their work
are misleading; in particular, it is well-known that in two dimensions a
circular boundary has a divergence in the Casimir energy for massless fields,
while for general dimension $D$ not equal to an even integer the corresponding
Casimir energy arising from massless fields interior and exterior to a
hyperspherical shell is finite. It has also long been recognized that the
Casimir energy for massive fields is divergent for $D\ne1$. These conclusions
are reinforced by a calculation of the relevant leading Feynman diagram in $D$
and three dimensions. There is therefore no doubt of the validity of the
conventional finite Casimir calculations.Comment: 25 pages, REVTeX4, 1 ps figure. Revision includes new subsection 4B
and Appendix, and other minor correction

### Scalar Casimir densities for cylindrically symmetric Robin boundaries

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
boundaries. It is assumed that the field obeys general Robin boundary
conditions on bounding surfaces. The application of a variant of the
generalized Abel-Plana formula allows to extract from the expectation values
the contribution from single shells and to present the interference part in
terms of exponentially convergent integrals. The vacuum forces acting on the
boundaries are presented as the sum of self-action and interaction terms. The
first one contains well-known surface divergences and needs a further
renormalization. The interaction forces between the cylindrical boundaries are
finite and are attractive for special cases of Dirichlet and Neumann scalars.
For the general Robin case the interaction forces can be both attractive or
repulsive depending on the coefficients in the boundary conditions. The total
Casimir energy is evaluated by using the zeta function regularization
technique. It is shown that it contains a part which is located on bounding
surfaces. The formula for the interference part of the surface energy is
derived and the energy balance is discussed.Comment: 22 pages, 5 figure

### Local and Global Casimir Energies: Divergences, Renormalization, and the Coupling to Gravity

From the beginning of the subject, calculations of quantum vacuum energies or
Casimir energies have been plagued with two types of divergences: The total
energy, which may be thought of as some sort of regularization of the
zero-point energy, $\sum\frac12\hbar\omega$, seems manifestly divergent. And
local energy densities, obtained from the vacuum expectation value of the
energy-momentum tensor, $\langle T_{00}\rangle$, typically diverge near
boundaries. The energy of interaction between distinct rigid bodies of whatever
type is finite, corresponding to observable forces and torques between the
bodies, which can be unambiguously calculated. The self-energy of a body is
less well-defined, and suffers divergences which may or may not be removable.
Some examples where a unique total self-stress may be evaluated include the
perfectly conducting spherical shell first considered by Boyer, a perfectly
conducting cylindrical shell, and dilute dielectric balls and cylinders. In
these cases the finite part is unique, yet there are divergent contributions
which may be subsumed in some sort of renormalization of physical parameters.
The divergences that occur in the local energy-momentum tensor near surfaces
are distinct from the divergences in the total energy, which are often
associated with energy located exactly on the surfaces. However, the local
energy-momentum tensor couples to gravity, so what is the significance of
infinite quantities here? For the classic situation of parallel plates there
are indications that the divergences in the local energy density are consistent
with divergences in Einstein's equations; correspondingly, it has been shown
that divergences in the total Casimir energy serve to precisely renormalize the
masses of the plates, in accordance with the equivalence principle.Comment: 53 pages, 1 figure, invited review paper to Lecture Notes in Physics
volume in Casimir physics edited by Diego Dalvit, Peter Milonni, David
Roberts, and Felipe da Ros

### Ambiguity in the evaluation of the effective action on the cone

An ambiguity in the computation of the one-loop effective action for fields
living on a cone is illustrated. It is shown that the ambiguity arises due to
the non-commutativity of the regularization of ultraviolet and (conical)
boundary divergencies.Comment: REVTeX file, 10 pages. Comments on recent papers have been adde