2,258 research outputs found
Analytic perturbation theory in QCD and Schwinger's connection between the beta-function and the spectral density
We argue that a technique called analytic perturbation theory leads to a
well-defined method for analytically continuing the running coupling constant
from the spacelike to the timelike region, which allows us to give a
self-consistent definition of the running coupling constant for timelike
momentum. The corresponding -function is proportional to the spectral
density, which confirms a hypothesis due to Schwinger.Comment: 11 pages, 2 figure
Attractive Casimir effect in an infrared modified gluon bag model
In this work, we are motivated by previous attempts to derive the vacuum
contribution to the bag energy in terms of familiar Casimir energy calculations
for spherical geometries. A simple infrared modified model is introduced which
allows studying the effects of the analytic structure as well as the geometry
in a clear manner. In this context, we show that if a class of infrared
vanishing effective gluon propagators is considered, then the renormalized
vacuum energy for a spherical bag is attractive, as required by the bag model
to adjust hadron spectroscopy.Comment: 7 pages. 1 figure. Accepted for publication in Physical Review D.
Revised version with improved analysis and presentation, references adde
Action of the gravitational field on the dynamical Casimir effect
In this paper we analyze the action of the gravitational field on the
dynamical Casimir effect. We consider a massless scalar field confined in a
cuboid cavity placed in a gravitational field described by a static and
diagonal metric. With one of the plane mirrors of the cavity allowed to move,
we compute the average number of particles created inside the cavity by means
of the Bogoliubov coefficients computed through perturbative expansions. We
apply our result to the case of an oscillatory motion of the mirror, assuming a
weak gravitational field described by the Schwarzschild metric. The regime of
parametric amplification is analyzed in detail, demonstrating that our computed
result for the mean number of particles created agrees with specific associated
cases in the literature. Our results, obtained in the framework of the
perturbation theory, are restricted, under resonant conditions, to a short-time
limit.Comment: 2 Figures, comments are welcom
Electromagnetic wave scattering by a superconductor
The interaction between radiation and superconductors is explored in this
paper. In particular, the calculation of a plane standing wave scattered by an
infinite cylindrical superconductor is performed by solving the Helmholtz
equation in cylindrical coordinates. Numerical results computed up to
of Bessel functions are presented for different wavelengths
showing the appearance of a diffraction pattern.Comment: 3 pages, 3 figure
Systematics of the Relationship between Vacuum Energy Calculations and Heat Kernel Coefficients
Casimir energy is a nonlocal effect; its magnitude cannot be deduced from
heat kernel expansions, even those including the integrated boundary terms. On
the other hand, it is known that the divergent terms in the regularized (but
not yet renormalized) total vacuum energy are associated with the heat kernel
coefficients. Here a recent study of the relations among the eigenvalue
density, the heat kernel, and the integral kernel of the operator
is exploited to characterize this association completely.
Various previously isolated observations about the structure of the regularized
energy emerge naturally. For over 20 years controversies have persisted
stemming from the fact that certain (presumably physically meaningful) terms in
the renormalized vacuum energy density in the interior of a cavity become
singular at the boundary and correlate to certain divergent terms in the
regularized total energy. The point of view of the present paper promises to
help resolve these issues.Comment: 19 pages, RevTeX; Discussion section rewritten in response to
referees' comments, references added, minor typos correcte
Ten years of the Analytic Perturbation Theory in QCD
The renormalization group method enables one to improve the properties of the
QCD perturbative power series in the ultraviolet region. However, it ultimately
leads to the unphysical singularities of observables in the infrared domain.
The Analytic Perturbation Theory constitutes the next step of the improvement
of perturbative expansions. Specifically, it involves additional analyticity
requirement which is based on the causality principle and implemented in the
K\"allen--Lehmann and Jost--Lehmann representations. Eventually, this approach
eliminates spurious singularities of the perturbative power series and enhances
the stability of the latter with respect to both higher loop corrections and
the choice of the renormalization scheme. The paper contains an overview of the
basic stages of the development of the Analytic Perturbation Theory in QCD,
including its recent applications to the description of hadronic processes.Comment: 26 pages, 9 figures, to be published in Theor. Math. Phys. (2007
The quantum metrology triangle and the re-definition of the SI ampere and kilogram; Analysis of a reduced set of observational equations
We have developed a set of seven observational equations that include all of
the physics necessary to relate the most important of the fundamental constants
to the definitions of the SI kilogram and ampere. We have used these to
determine the influence of alternative definitions being considered for the SI
kilogram and ampere on the uncertainty of three of the fundamental constants
(h, e and mu). We have also reviewed the experimental evidence for the
exactness of the quantum metrology triangle resulting from experiments
combining the quantum Hall effect, the Josephson effects and single-electron
tunnelling.Comment: 16 pages, 3 figures & 5 table
Electromagnetic Casimir piston in higher dimensional spacetimes
We consider the Casimir effect of the electromagnetic field in a higher
dimensional spacetime of the form , where is the
4-dimensional Minkowski spacetime and is an -dimensional
compact manifold. The Casimir force acting on a planar piston that can move
freely inside a closed cylinder with the same cross section is investigated.
Different combinations of perfectly conducting boundary conditions and
infinitely permeable boundary conditions are imposed on the cylinder and the
piston. It is verified that if the piston and the cylinder have the same
boundary conditions, the piston is always going to be pulled towards the closer
end of the cylinder. However, if the piston and the cylinder have different
boundary conditions, the piston is always going to be pushed to the middle of
the cylinder. By taking the limit where one end of the cylinder tends to
infinity, one obtains the Casimir force acting between two parallel plates
inside an infinitely long cylinder. The asymptotic behavior of this Casimir
force in the high temperature regime and the low temperature regime are
investigated for the case where the cross section of the cylinder in is
large. It is found that if the separation between the plates is much smaller
than the size of , the leading term of the Casimir force is the
same as the Casimir force on a pair of large parallel plates in the
-dimensional Minkowski spacetime. However, if the size of
is much smaller than the separation between the plates, the leading term of the
Casimir force is times the Casimir force on a pair of large parallel
plates in the 4-dimensional Minkowski spacetime, where is the first Betti
number of . In the limit the manifold vanishes, one
does not obtain the Casimir force in the 4-dimensional Minkowski spacetime if
is nonzero.Comment: 22 pages, 4 figure
Source amplitudes for active exterior cloaking
The active cloak comprises a discrete set of multipole sources that
destructively interfere with an incident time harmonic scalar wave to produce
zero total field over a finite spatial region. For a given number of sources
and their positions in two dimensions it is shown that the multipole amplitudes
can be expressed as infinite sums of the coefficients of the incident wave
decomposed into regular Bessel functions. The field generated by the active
sources vanishes in the infinite region exterior to a set of circles defined by
the relative positions of the sources. The results provide a direct solution to
the inverse problem of determining the source amplitudes. They also define a
broad class of non-radiating discrete sources.Comment: 21 pages, 17 figure
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