4,969 research outputs found
Casimir Energies and Pressures for -function Potentials
The Casimir energies and pressures for a massless scalar field associated
with -function potentials in 1+1 and 3+1 dimensions are calculated. For
parallel plane surfaces, the results are finite, coincide with the pressures
associated with Dirichlet planes in the limit of strong coupling, and for weak
coupling do not possess a power-series expansion in 1+1 dimension. The relation
between Casimir energies and Casimir pressures is clarified,and the former are
shown to involve surface terms. The Casimir energy for a -function
spherical shell in 3+1 dimensions has an expression that reduces to the
familiar result for a Dirichlet shell in the strong-coupling limit. However,
the Casimir energy for finite coupling possesses a logarithmic divergence first
appearing in third order in the weak-coupling expansion, which seems
unremovable. The corresponding energies and pressures for a derivative of a
-function potential for the same spherical geometry generalizes the TM
contributions of electrodynamics. Cancellation of divergences can occur between
the TE (-function) and TM (derivative of -function) Casimir
energies. These results clarify recent discussions in the literature.Comment: 16 pages, 1 eps figure, uses REVTeX
Green's Dyadic Approach of the Self-Stress on a Dielectric-Diamagnetic Cylinder with Non-Uniform Speed of Light
We present a Green's dyadic formulation to calculate the Casimir energy for a
dielectric-diamagnetic cylinder with the speed of light differing on the inside
and outside. Although the result is in general divergent, special cases are
meaningful. It is pointed out how the self-stress on a purely dielectric
cylinder vanishes through second order in the deviation of the permittivity
from its vacuum value, in agreement with the result calculated from the sum of
van der Waals forces.Comment: 8 pages, submitted to proceedings of QFEXT0
How does Casimir energy fall? III. Inertial forces on vacuum energy
We have recently demonstrated that Casimir energy due to parallel plates,
including its divergent parts, falls like conventional mass in a weak
gravitational field. The divergent parts were suitably interpreted as
renormalizing the bare masses of the plates. Here we corroborate our result
regarding the inertial nature of Casimir energy by calculating the centripetal
force on a Casimir apparatus rotating with constant angular speed. We show that
the centripetal force is independent of the orientation of the Casimir
apparatus in a frame whose origin is at the center of inertia of the apparatus.Comment: 8 pages, 2 figures, contribution to QFEXT07 proceeding
The Bjorken Sum Rule in the Analytic Approach to Perturbative QCD
Results of applying analytic perturbation theory (APT) to the Bjorken sum
rule are presented. We study the third-order QCD correction within the analytic
approach and investigate its renormalization scheme dependence. We demonstrate
that, in the framework of the method, theoretical predictions of the Bjorken
sum rule are, practically, scheme independent for the entire interval of
momentum transfer.Comment: 12 pages, 3 eps figures, uses elsart.cl
Analytic Perturbation Theory: A New Approach to the Analytic Continuation of the Strong Coupling Constant into the Timelike Region
The renormalization group applied to perturbation theory is ordinarily used
to define the running coupling constant in the spacelike region. However, to
describe processes with timelike momenta transfers, it is important to have a
self-consistent determination of the running coupling constant in the timelike
region. The technique called analytic perturbation theory (APT) allows a
consistent determination of this running coupling constant. The results are
found to disagree significantly with those obtained in the standard
perturbative approach. Comparison between the standard approach and APT is
carried out to two loops, and threshold matching in APT is applied in the
timelike region.Comment: 16 pages, REVTeX, 7 postscript figure
Remark on the perturbative component of inclusive -decay
In the context of the inclusive -decay, we analyze various forms of
perturbative expansions which have appeared as modifications of the original
perturbative series. We argue that analytic perturbation theory, which combines
renormalization-group invariance and -analyticity, has significant merits
favoring its use to describe the perturbative component of -decay.Comment: 5 pages, ReVTEX, 2 eps figures. Revised paper includes clarifying
remarks and corrected references. To be published in Phys. Rev.
Wightman function and vacuum fluctuations in higher dimensional brane models
Wightman function and vacuum expectation value of the field square are
evaluated for a massive scalar field with general curvature coupling parameter
subject to Robin boundary conditions on two codimension one parallel branes
located on -dimensional background spacetime
with a warped internal space . The general case of different Robin
coefficients on separate branes is considered. The application of the
generalized Abel-Plana formula for the series over zeros of combinations of
cylinder functions allows us to extract manifestly the part due to the bulk
without boundaries. Unlike to the purely AdS bulk, the vacuum expectation value
of the field square induced by a single brane, in addition to the distance from
the brane, depends also on the position of the brane in the bulk. The brane
induced part in this expectation value vanishes when the brane position tends
to the AdS horizon or AdS boundary. The asymptotic behavior of the vacuum
densities near the branes and at large distances is investigated. The
contribution of Kaluza-Klein modes along is discussed in various
limiting cases. As an example the case is considered,
corresponding to the bulk with one compactified dimension. An
application to the higher dimensional generalization of the Randall-Sundrum
brane model with arbitrary mass terms on the branes is discussed.Comment: 25 pages, 2 figures, discussion added, accepted for publication in
Phys.Rev.
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