16251774
Spectral zeta functions for a cylinder and a circle
Spectral zeta functions ζ(s) for the massless scalar fields obeying the Dirichlet and Neumann boundary conditions on a surface of an infinite cylinder are constructed. These functions are defined explicitly in a finite domain of the complex plane s containing the closed interval of real axis −1⩽Re s⩽0. Proceeding from this the spectral zeta functions for the boundary conditions given on a circle (boundary value problem on a plane) are obtained without any additional calculations. The Casimir energy for the relevant field configurations is deduced.
29489956
Direct mode summation for the Casimir energy of a solid ball
The Casimir energy of a solid ball placed in an infinite medium is calculated by a direct frequency summation using the contour integration. It is assumed that the permittivity and permeability of the ball and medium satisfy the condition . After deriving the general expression for the Casimir energy, a compact ball is considered when . Calculations are carried out which are of the first order in and take account of the fifth-order terms in the uniform asymptotic expansion of the Bessel functions involved. The implication of the results to attempt to explain sonoluminescence via the Casimir effect is briefly discussed.
15884859
Casimir energy of a nonuniform string
The Casimir energy of a non-uniform string built up from two pieces with different speed of sound is calculated. A standard procedure of subtracting the energy of an infinite uniform string is applied, the subtraction being interpreted as the renormalization of the string tension. It is shown that in the case of a homogeneous string this method is completely equivalent to the zeta renormalization.
121905919
Eikonal approximation for high-energy inclusive processes
126085042
ON THE INTERPRETATION OF THE NOETHER IDENTITIES
118320834
Surface modes and photonic modes in Casimir calculations for a compact cylinder
A rigorous formulation of the problem of calculating the electromagnetic vacuum energy of an infinite dielectric cylinder is discussed. It is shown that the physically relevant spectrum of electromagnetic excitations includes the surface modes and photonic modes. The mathematical procedure of summing over this spectrum is proposed, and the transition to imaginary frequencies is accomplished. As a result, the imaginary-frequency representation for the vacuum energy is justified which has been used in previous Casimir studies for this configuration.
116346471
APPLICATION OF NUCLEAR THEORY METHODS TO NEW FAMILY OF FERMI SYSTEM
Duo to a remarkable progress in experimental techniques, the new family of .small Fermi systems (SFS) (metal clusters, fullerencs, helium clusters and quantum dots) was discovered about ten years ago. As was established, those Fermi systems have a striking similarity with atomic nuclei (see re­views and conference proceedings [1-9]). The most remarkable feature of now SFS is that they possess a mean field of the same kind as in atomic iniclci which allows one to investigate SFS by nuclear theory methods. If recent investigations of SFS have mainly been limited to atoms and atomic nuclei, our present possibilities have become much wider, We have really obtained a good chance for studying both a common behavior of SFS and a wonderful variety of their properties. In the present paper, the particular properties of the new SFS as well as the application of nuclear physics methods to their description are briefly reviewed. The properties of the new SFS and atomic nuclei are continually compared. The main attention is paid to metal clusters (MC) or, more precisely, to E\ giant resonances (GR) in this system. Iri Sec.2, the sketch of basic properties of MC as well as the perspectives of their investigation arc given. Sec.3 is devoted to the description of E\ GR in MC, In Sec.3 the properties of fullerencs, helium clusters and quantum dots are outlined. In Sec.4 the conclusions are presented.
125323640
{QCD} Sum Rule Analysis of the Pion Form-factor Behavior in Small $Q^2$ Region
118213659
Pion form factor in a scalar model
SummaryUsing as an example the simple scalar modelρ(6)3; we describe our method of analysing the bound-state form factors based on the systematic use of the alpha-representation for Feynman diagrams. The nature of «nonrenormalization group» logarithms specific for the form-factor-type problems is investigated. The summation of ladder contributions is performed in the leading-logarithm approximation.RiassuntoUsando come esempio il semplice modello scalareρ(6)3 si descrive il metodo di analizzare i fattori di forma dello stato legato basati sull’uso sistematico della rappresentazione alfa per i diagrammi di Feyman. Si studia la natura dei logaritmi del gruppo di non rinormalizzazione specifico di problemi di tipo fattore di forma. Si esegue la somma dei contributi di a gradini nell’approssimazione del logaritmo principale.РезюмеНа примере простой скалярной моделиρ(6)3 излагается метод анализа формфакторов составных систем, основанный на систематическом использовании альфа-представления фейнмановских диаграмм. Исследуется природа «неренормгрупповых» логарифмов, специфичных для задач формфакторного типа. Проведено суммирование лестничных вкладов в главном лограрифмическом приближении.
120815334
Local Quark - Hadron Duality and Nucleon Form-factors in {QCD}
Abstract Quark-hadron duality is incorporated to estimate the non-perturbative O(α 0 S -contribution to the nucleon form factors G N E,M ( t ). For 1 t 2 the results are in satisfactory agreement with the existing data. This means that the observed dipole behaviour of G N ( t ) has nothing to do with the short distance dynamics.
120836438
Quantum gravitational effects in an isotropic universe
Effects of vacuum polarization by an external gravitational field in a system of spinor, scalar, and massive vector particles are considered in the model of conformally flat space-time. Expressions are obtained for the radiative corrections, and the part they play in gravitational theory is analyzed in the limits of weak (Vertical BarR/sup k//sub i/Vertical Bar m/sup 2/) gravitational fields. The Appendix gives expressions for the rate of spontaneous production of real particles by a strong gravitational field and the energy-momentum tensor of real particles in the ultrarelativistic limit; a law of increase of the entropy of an ultrarelativistic medium is also formulated.