Volume 6, Issue 22 (October 2009)

Number 

Articles Title

Abstract

1

Foreword

Ignazio Licata

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2

Equivalence Principle and Field Quantization in Curved Spacetime

H. Kleinert

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To comply with the equivalence principle, fields in curved spacetime can be quantized only in the neighborhood of each point, where one can construct a freely falling Minkowski frame with zero curvature. In each such frame, the geometric forces of gravity can be replaced by a selfinteracting spin-2 field, as proposed by Feynman in 1962. At a fixed distance $R$ from a black hole, the vacuum in each freely falling volume element acts like a thermal bath of all particles with Unruh temperature T_U=\hbar GM/2\pi c R^2. At the horizon R=2GM/c^2, the falling vacua show the Hawking temperature T_H=\hbar c^3/8\pi GMk_B

3

New Seiberg-Witten Fields Maps Through Weyl Symmetrization and the Pure Geometric Extension of The Standard Model

N. Mebarki; F. Khelili and O. Benabbes

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A unified description of a symmetrized and anti-symmetrized Moyal star product of the noncommutative infinitesimal gauge transformations is presented and the corresponding Seiberg-Witten maps are derived. Moreover, the noncommutative covariant derivative, field strength tensor as well as gauge transformations are shown to be consistently constructed not on the enveloping but on the Lie and/or Poisson algebra. As an application, a pure geometric extension of the standard model is shown explicitly.

4

A Method for Constructing a Lax Pair for the Ernst Equation

C. J. Papachristou  and B. Kent Harrison

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A systematic construction of a Lax pair and an infinite set of conservation laws for the Ernst equation is described. The matrix form of this equation is rewritten as a differential ideal of (2,R)-valued differential forms, and its symmetry condition is expressed as an exterior equation which is linear in the symmetry characteristic and has the form of a conservation law. By means of a recursive process, an infinite collection of such laws is then obtained, and the conserved ``charges'' are used to derive a linear exterior equation whose components constitute a Lax pair.

5

Plane Symmetric Viscous Fluid Universe in Lyra Geometry

Pratima Singh  and Pawan Kumar Rai

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A new class of plane-symmetric homogeneous cosmological models for viscous fluid distribution is obtained in the context of Lyra's geometry. We have obtained two types of solutions by considering the uniform as well as time dependent displacement field. To get the deterministic solutions of Einstein's modified field equations, the free gravitational field is assumed to be of type D which is of the next order in the hierarchy of Petrov classification. It has been found that the displacement vector $\beta$ behaves like cosmological term \Lambda in the normal gauge treatment and the solutions are consistent with the observations. The displacement vector \beta(t) affects entropy. Some physical and geometric properties of the models are discussed.

6

Some Bianchi Type I Cosmological Models of the Universe for Viscous Fluid Distribution in Lyra Geometry

Ravi Prakash Singh and Lallan Yadav

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Some Bianchi type I cosmological models of the universe with time dependent gauge function $\beta$ for viscous fluid distribution within the framework of Lyra geometry are investigated in which the expansion is considered only in two dimensions i.e. one of the Hubble parameter (H_{1} = \frac{\dot{A}}{A}) is zero. To get the deterministic solutions of Einstein's modified field equations, the viscosity coefficient of bulk viscous fluid is assumed to be a power function of mass density and the coefficient of shear viscosity is considered as constant in first case whereas in other case it is taken as proportional to scale of expansion in the model. It has been found that the displacement vector \beta(t) behaves like cosmological term \Lambda in the normal gauge treatment and the solutions are consistent with the observations. Solution in absence of shear viscosity is also obtained. The displacement vector \beta(t) affects entropy. Some physical and geometrical properties of the models are discussed.

7

Geometrical Behaviuors of LRS Bianchi Type-I Cosmological Model

Hassan Amirhashchi, Hishamuddin Zainuddin and Hamid Nil Saz Dezfouli

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By using Einstein's theory of general relativity some properties of spatially homogeneous locally rotationally symmetric (LRS) Bianchi type-I space-time are investigated in empty space. The concept of Riemannian curvature tensor, Ricci tensor and Ricci scalar has been used to discuss the geometrical behavior of the space-time. It is shown that, LRS Bianchi type-I has always flat geometry in empty space. Also we have shown that the vacuum model does not have singularity when time goes to zero.

8

Bianchi Type V Bulk Viscous Cosmological Models with Time Dependent Lambda Λ Term

J. P. Singh and P. S. Baghel

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Spatially homogeneous and anisotropic Bianchi type V space-time with bulk viscous fluid source and time-dependent cosmological term are considered. Cosmological models have been obtained by assuming a variation law for the Hubble parameter which yields a constant value of deceleration parameter. Physical and kinematical parameters of the models are discussed. The models are found to be compatible with the results of cosmological observations.

9

Corrections to massive neutrino masses, caused by vacuum polarisation in strong Coulomb field of daughter nuclei in weak decays of heavy ions

N. Ivanov, P. Kienle, E. L. Kryshen,  and M. Pitschmann

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We calculate corrections to masses of massive neutrino   mass--eigenstates, caused by vacuum polarization in the strong  Coulomb fields of daughter heavy nuclei in the K--shell electron  capture decays (EC) and positron (\beta^+) decays of highly  ionized heavy ions, investigated experimentally at GSI in  Darmstadt. Some applications of the obtained results are discussed.

10

Neutrino Mass Differences and Nonunitarity of Neutrino Mixing Matrix from Interfering Recoil Ions

H. Kleinert  and P. Kienle

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We show that the recent observation of the time modulation of two-body weak decays of heavy ions reveals the  mass content  of the electron neutrinos via interference patterns in the recoiling ion wave function. From the modulation period we derive the difference of the square masses \Delta m^2\approx 22.5\times 10^{-5}$\,eV${}^2, which is about 2.8 times larger than that derived from a combined analysis of KamLAND and solar neutrino oscillation experiments. It is, however, compatible with a data regime to which the KamLAND analysis attributes a smaller probability. The experimental results displayed in Fig.~1 imply that the neutrino mixing matrix violates unitarity by about 10\%.

11

Bifurcations of fractional-order diffusionless Lorenz system

Kehui Sun and J. C. Sprott

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Using the predictor-corrector scheme, the fractional-order diffusionless Lorenz system is investigated numerically. The effective chaotic range of the fractional-order diffusionless system for variation of the single control parameter is determined. The route to chaos is by period-doubling bifurcation in this fractional-order system, and some typical bifurcations are observed, such as the flip bifurcation, the tangent bifurcation, an interior crisis bifurcation, and transient chaos. The results show that the fractional-order diffusionless Lorenz system has complex dynamics with interesting characteristics.

12

Underdeterminacy and redundance in Maxwell’s Equations

Peter Enders

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Maxwell's (1864) original equations are redundant in their description of charge conservation. In the nowadays used, 'rationalized' Maxwell equations, this redundancy is removed through omitting the continuity equation. Alternatively, one can Helmholtz decompose the original set and omit instead the longitudinal part of the flux law. This provides at once a natural description of the transversality of free electromagnetic waves and paves the way to eliminate the gauge freedom. Poynting's inclusion of the longitudinal field components in his theorem represents an additional assumption to the Maxwell equations. Further, exploiting the concept of Newtonian and Laplacian vector fields, the role of the static longitudinal component of the vector potential being \emph{not} determined by Maxwell's equations, but important in quantum mechanics (Aharonov-Bohm effect) is elucidated. Finally, extending Messiah's (1999) description of a gauge invariant canonical momentum, a manifest gauge invariant canonical formulation of Maxwell's theory \emph{without} imposing any contraints or auxiliary conditions will be proposed as input for Dirac's (1949) approach to special-relativistic dynamics.

13

The Proton as A Kerr-Newman Black Hole

Robert L. Oldershaw

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The general equation governing the mass, spin and angular momentum of a Kerr-Newman black hole applies equally well to a proton when the gravitational coupling constant predicted by a discrete fractal paradigm is used in the equation, along with the standard mass, spin and angular momentum of the proton.

14

Self-Interacting Scalar Field and Galactic Dark Halos

M. R. Bordbar and N. Riazi

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We construct dark halo models which are supported by a self-interacting scalar field. The possibility that the energy density of such a field which could produce dark matter and dark energy inside and outside of the galactic dark halos is explored.

15

Path Integral Quantization of The Electromagnetic Field Coupled to A Spinor

Walaa. I. Eshraim and Nasser. I. Farahat

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The Hamilton-Jacobi approach is applied to the electromagnetic field coupled to a spinor. The integrability conditions are investigated and the path integral quantization is performed using the action given by Hamilton-Jacobi approach.

16

Neutrino Mixing and Cosmological Constant above GUT Scale

Bipin Singh Koranga

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Neutrino mixing lead to a non zero contribution to the cosmological constant. We consider non renormalization $1/M_{x}$ interaction term as a perturbation of the neutrino mass matrix. We find that for the degenerate neutrino mass spectrum. We assume that the neutrino masses and mixing arise through physics at a scale intermediate between Planck Scale and the electroweak scale. We also assume, above the electroweak breaking scale, neutrino masses are nearly degenerate and their mixing is bimaximal. Quantum gravitational (Planck scale) effects lead to an effective $SU(2)_{L}\times U(10$ invariant dimension-5 Lagrangian involving neutrino and Higgs fields, which gives rise to additional terms in neutrino mass matrix. There additional term can be considered to be perturbation of the GUT scale bi-maximal neutrino mass matrix. We assume that the gravitational interaction is flavour blind and we study the neutrino mixing and cosmological constant due to physics above the GUT scale.

17

The Restricted Three Body Problem with Quadratic Drag

Mayer Humi

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When an asteroid, space-craft or another small object in the solar system is in the vicinity of a planet it is subjected to the gravitational forces of the Sun, the planet, the drag forces due to the solar wind and (possibly) the planet upper atmosphere. To determine the object trajectory we consider this problem within the context of the restricted three body problem in three dimensions with quadratic drag. In this setting we linearize the equations of motion of the object and cast them in a coordinate system with respect to the secondary (planet) which is assumed to be in a general Keplerian orbit around the primary (Sun). We then reduce them, to a simple system of three second order linear differential equations. These equations can be considered to be a generalization of Hill's equations to general Keplerian orbits (of the secondary) with the addition of quadratic drag force acting on the third object in the system. We derive also "approximate conservation laws" in three dimensions which represent a generalization of Jacobi's integral in two dimensions and consider some special cases.