141 research outputs found

### Remark on the perturbative component of inclusive $\tau$-decay

In the context of the inclusive $\tau$-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 $Q^2$-analyticity, has significant merits
favoring its use to describe the perturbative component of $\tau$-decay.Comment: 5 pages, ReVTEX, 2 eps figures. Revised paper includes clarifying
remarks and corrected references. To be published in Phys. Rev.

### Can the QCD Effective Charge Be Symmetrical in the Euclidean and the Minkowskian Regions?

We study a possible symmetrical behavior of the effective charges defined in
the Euclidean and Minkowskian regions and prove that such symmetry is
inconsistent with the causality principle.Comment: 5 pages, REVTe

### The Casimir Problem of Spherical Dielectrics: Quantum Statistical and Field Theoretical Approaches

The Casimir free energy for a system of two dielectric concentric nonmagnetic
spherical bodies is calculated with use of a quantum statistical mechanical
method, at arbitrary temperature. By means of this rather novel method, which
turns out to be quite powerful (we have shown this to be true in other
situations also), we consider first an explicit evaluation of the free energy
for the static case, corresponding to zero Matsubara frequency ($n=0$).
Thereafter, the time-dependent case is examined. For comparison we consider the
calculation of the free energy with use of the more commonly known field
theoretical method, assuming for simplicity metallic boundary surfaces.Comment: 31 pages, LaTeX, one new reference; version to appear in Phys. Rev.

### New analytic running coupling in spacelike and timelike regions

The new model for the QCD analytic running coupling, proposed recently, is
extended to the timelike region. This running coupling naturally arises under
unification of the analytic approach to QCD and the renormalization group (RG)
formalism. A new method for determining the coefficients of the "analytized" RG
equation is elaborated. It enables one to take into account the higher loop
contributions to the new analytic running coupling (NARC) in a consistent way.
The expression for the new analytic running coupling, independent of the
normalization point, is obtained by invoking the asymptotic freedom condition.
It is shown that the difference between the values of the NARC in respective
spacelike and timelike regions is rather valuable for intermediate energies.
This is essential for the correct extracting of the running coupling from
experimental data. The new analytic running coupling is applied to the
description of the inclusive $\tau$ lepton decay. The consistent estimation of
the parameter $\Lambda_{QCD}$ is obtained here.Comment: REVTeX 3.1, 12 pages with 3 EPS figures; enlarged version is
published in Phys. Rev.

### 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

### Double-delta potentials: one dimensional scattering. The Casimir effect and kink fluctuations

The path is explored between one-dimensional scattering through
Dirac-$\delta$ walls and one-dimensional quantum field theories defined on a
finite length interval with Dirichlet boundary conditions. It is found that two
$\delta$'s are related to the Casimir effect whereas two $\delta$'s plus the
first transparent P$\ddot{\rm o}$sch-Teller well arise in the context of the
sine-Gordon kink fluctuations, both phenomena subjected to Dirichlet boundary
conditions. One or two delta wells will be also explored in order to describe
absorbent plates, even though the wells lead to non unitary Quantum Field
Theories.Comment: 15 pages. To be published in the International Journal of Theoretical
Physic

### 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

### Global vs local Casimir effect

This paper continues the investigation of the Casimir effect with the use of
the algebraic formulation of quantum field theory in the initial value setting.
Basing on earlier papers by one of us (AH) we approximate the Dirichlet and
Neumann boundary conditions by simple interaction models whose nonlocality in
physical space is under strict control, but which at the same time are
admissible from the point of view of algebraic restrictions imposed on models
in the context of Casimir backreaction. The geometrical setting is that of the
original parallel plates. By scaling our models and taking appropriate limit we
approach the sharp boundary conditions in the limit. The global force is
analyzed in that limit. One finds in Neumann case that although the sharp
boundary interaction is recovered in the norm resolvent sense for each model
considered, the total force per area depends substantially on its choice and
diverges in the sharp boundary conditions limit. On the other hand the local
energy density outside the interaction region, which in the limit includes any
compact set outside the strict position of the plates, has a universal limit
corresponding to sharp conditions. This is what one should expect in general,
and the lack of this discrepancy in Dirichlet case is rather accidental. Our
discussion pins down its precise origin: the difference in the order in which
scaling limit and integration over the whole space is carried out.Comment: 32 pages, accepted for publication in Ann. H. Poincar

### The Dirichlet Casimir effect for $\phi^4$ theory in (3+1) dimensions: A new renormalization approach

We calculate the next to the leading order Casimir effect for a real scalar
field, within $\phi^4$ theory, confined between two parallel plates in three
spatial dimensions with the Dirichlet boundary condition. In this paper we
introduce a systematic perturbation expansion in which the counterterms
automatically turn out to be consistent with the boundary conditions. This will
inevitably lead to nontrivial position dependence for physical quantities, as a
manifestation of the breaking of the translational invariance. This is in
contrast to the usual usage of the counterterms in problems with nontrivial
boundary conditions, which are either completely derived from the free cases or
at most supplemented with the addition of counterterms only at the boundaries.
Our results for the massive and massless cases are different from those
reported elsewhere. Secondly, and probably less importantly, we use a
supplementary renormalization procedure, which makes the usage of any analytic
continuation techniques unnecessary.Comment: JHEP3 format,20 pages, 2 figures, to appear in JHE

### Casimir energy of a compact cylinder under the condition $\epsilon\mu = c^{-2}$

The Casimir energy of an infinite compact cylinder placed in a uniform
unbounded medium is investigated under the continuity condition for the light
velocity when crossing the interface. As a characteristic parameter in the
problem the ratio $\xi^2=(\epsilon_1-\epsilon_2)^2/ (\epsilon_1+\epsilon_2)^-2
= (\mu_1-\mu_2)^2/(\mu_1+ \mu_2)^2 \le 1$ is used, where $\epsilon_1$ and
$\mu_1$ are, respectively, the permittivity and permeability of the material
making up the cylinder and $\epsilon_2$ and $\mu_2$ are those for the
surrounding medium. It is shown that the expansion of the Casimir energy in
powers of this parameter begins with the term proportional to $\xi^4$. The
explicit formulas permitting us to find numerically the Casimir energy for any
fixed value of $\xi^2$ are obtained. Unlike a compact ball with the same
properties of the materials, the Casimir forces in the problem under
consideration are attractive. The implication of the calculated Casimir energy
in the flux tube model of confinement is briefly discussed.Comment: REVTeX, 12 pages, 1 figure in a separate fig1.eps file, 1 table;
minor corrections in English and misprints; version to be published in Phys.
Rev. D1

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