Remark on the perturbative component of inclusive τ\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 ϕ4\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 ϵμ=c−2\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