Regular Series


Vol. 39 (2008), No. 4, pp. 753 – 995


Erweiterungen inhomogener Lie-Algebren und deren Casimir-Invarianten. Anwendungen auf die inhomogene Weyl-Algebra (Extension of Inhomogenous Lie Algebras and Their Casimir Invariants. Application to the Inhomogenous Weyl Algebra)

abstract

Wir untersuchen die Struktur der Casimiroperatoren inhomogener Lie-Algebren \(\mathfrak {g}=\mathfrak {s}\overrightarrow {\oplus }_{{\mit \Lambda }}nL_{1}\) in bezug auf die Variablen des Radikals. Es wird die Existenz einer Erweiterung gezeigt, dessen Invarianten als rationale Funktionen der Casimiroperatoren von \(\mathfrak {g}\) darstellbar sind. Spezifisch wird bewiesen, daß die Casimiroperatoren der inhomogenen Lie-Algebren \(\mathfrak {s}\overrightarrow {\oplus }_{{\mit \Lambda }}nL_{1}\) homogene Polynome in den Translationsvariablen sind. Daraus folgt ein Unabhängigkeitskriterium für Casimiroperatoren inhomogener Algebren. Als weitere Anwendung wird gezeigt, daß die Invarianten der inhomogenen Weyl-Algebra \(W(p,q)\) der Feldtheorie als einfache Quotienten der Casimiroperatoren von \(I\mathfrak {so}(p,q)\) gewählt werden können.


Particle Creation in Oscillating Cavities with Cubic and Cylindrical Geometry

abstract

In the present paper we study the creation of massless scalar particles from the quantum vacuum due to the dynamical Casimir effect by oscillating cavities with cubic and cylindrical geometry. To the first order of the amplitude we derive the expressions for the number of the created particles.


On Energy of the Friedman Universes in Conformally Flat Coordinates

abstract

Recently many authors have calculated energy of the Friedman universes by using coordinate-dependent double index energy-momentum complexes in Cartesian comoving coordinates \((t,x,y,z)\) and concluded that the flat and closed Friedman universes are energy-free. In this paper by using Einstein canonical energy-momentum complex and by doing calculations in conformally flat coordinates we show that such conclusion is incorrect. The results obtained in this paper are compatible with the results of our previous paper, see J. Garecki, Found. Phys. 37, 341 (2007), where we have used coordinate-independent averaged energy-momentum tensors to analyze the energy of Friedman universes.


Diagrammatic Approach to Fluctuations in the Wishart Ensemble

abstract

Using diagrammatic techniques, we calculate two-point Green’s function for complex Wishart ensemble.


Relativity without Tears

abstract

Special relativity is no longer a new revolutionary theory but a firmly established cornerstone of modern physics. The teaching of special relativity, however, still follows its presentation as it unfolded historically, trying to convince the audience of this teaching that Newtonian physics is natural but incorrect and special relativity is its paradoxical but correct amendment. I argue in this article in favor of logical instead of historical trend in teaching of relativity and that special relativity is neither paradoxical nor correct (in the absolute sense of the nineteenth century) but the most natural and expected description of the real space-time around us valid for all practical purposes. This last circumstance constitutes a profound mystery of modern physics better known as the cosmological constant problem.


Solutions of Massless Conformal Scalar Field in an \(n\)-Dimensional Einstein Space

abstract

In this paper the wave equation for massless conformal scalar field in an Einstein’s \(n\)-dimensional universe is solved and the eigen frequencies are obtained. The special case for \(\alpha = 4\) is recovered and the results are in exact agreement with those obtained in literature.


Hierarchically Organized Iterative Solutions of the Evolution Equations in QCD

abstract

The task of Monte Carlo simulation of the evolution of the parton distributions in QCD and of constructing new parton shower Monte Carlo algorithms requires new way of organizing solutions of the QCD evolution equations, in which quark–gluon transitions on the one hand and quark–quark or gluon–gluon transitions (pure gluonstrahlung) on the other hand, are treated separately and differently. This requires certain reorganization of the iterative solutions of the QCD evolution equations and leads to what we refer to as a hierarchic iterative solutions of the evolution equations. We present three formal derivations of such a solution. Results presented here are already used in the other recent works to formulate new MC algorithms for the parton-shower-like implementations of the QCD evolution equations. They are primarily of the non-Markovian type. However, such a solution can be used for the Markovian-type MCs as well. We also comment briefly on the relation of the presented formalism to similar methods used in other branches of physics.


Suppression of Statistical Background in the Event Structure of Away-Side \(\Delta \phi \) Distribution

abstract

An approach is proposed to analyze the azimuthal distribution of particles produced on the away side in heavy-ion collisions without background subtraction. Measures in terms of factorial moments are suggested that can suppress the statistical background, while giving clear distinction between one-jet and two-jet event structures on the away side. It is also possible to map the position and strength of the recoil jet to suitably chosen asymmetry moments.


Overlap Integrals Between Atomic Orbitals with Piecewise Polynomial Radial Part Evaluated in Prolate Spheroidal Coordinates

abstract

The algorithm evaluating the overlap integrals for the numerical atomic orbitals is presented. The general class of atomic orbitals is discussed, where the radial part of the atomic orbital is represented as a piecewise polynomial and the angular part is a complex spherical harmonic. The molecular problem is reduced to the diatomic case, which is solved in prolate spheroidal coordinate system. In the prolate spheroidal coordinates, the overlap integral is reduced to the integral over the polygon. The application of the piecewise polynomial representation of the radial part further reduces the complexity of the problem. Finally, it is shown that the integral can be obtained analytically for \(s,~p,~d\) orbitals.


Plasma Electromagnetic Fluctuations as an Initial Value Problem

abstract

Fluctuations of electric and magnetic fields in the collisionless plasma are found as a solution of the initial value linearized problem. The plasma initial state is on average stationary and homogeneous. When the state is stable, the initial fluctuations decay exponentially and in the long time limit a stationary spectrum of fluctuations is established. For the equilibrium plasma it reproduces the spectrum obtained from the fluctuation-dissipation relation. Fluctuations in the unstable two-stream system are also discussed.


The Correlations Among Color, Morphology, and Luminosity for the Main Galaxy Sample of the SDSS Data Release 5

abstract

Using the Main galaxy sample of the SDSS Data Release 5, we have investigated the correlations among color, morphology, and luminosity. We find that only within certain luminosity region the proportion of early-type galaxies significantly increases with increasing luminosity. The CM relations of galaxies also do not present single tendency, for different CM relations or in different luminosity regions, the tendencies of changes of the mean colors with luminosity are different. The mean colors of galaxies significantly increase with increasing luminosity only within certain luminosity region for some CM relations. Within certain color region the proportion of early-type galaxies also increases with increasing colors-especially for \(g\)–\(r\) color. For very blue galaxies, the proportion of early-type is weak functions of colors except \(u\)–\(g\) color. For the reddest galaxies the early-type proportion decreases with increasing colors.


The Big Bang Quantum Cosmology: The Matter-Energy Production Epoch

abstract

The exactly solvable quantum model of the homogeneous, isotropic and closed universe in the matter-energy production epoch is considered. It is assumed that the universe is originally filled with a uniform scalar field and a perfect fluid which defines a reference frame. The stationary state spectrum and the wave functions of the quantum universe are calculated. In this model the matter-energy in the universe has a component in the form of a condensate of massive zero-momentum excitation quanta of oscillations of primordial scalar field. The mean value of the scale factor of the universe in a given state is connected with the mass of a condensate by a linear relation. The nucleation rate of the universe from the initial cosmological singularity point is calculated. It is demonstrated that the process of nucleation of the universe can have an exponential (explosive) nature. The evolution of the universe is described as transitions with non-zero probabilities between the states of the universe with different masses of a condensate.


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