Regular Series


Vol. 38 (2007), No. 6, pp. 1979 – 2220


Study of Cosmological Model Bianchi I in the Conformal Poincaré-Gauge Theory of Gravitation

abstract

The equations for Bianchi I cosmology in the conformal Poincaré-gauge theory of gravitation are considered. It is shown that in case of anisotropy on two directions it is impossible to construct model with a matter satisfying standard physical requirements. The exact vacuum solution corresponding to “pancakes of Zel’dovich” is found.


Probabilistic Teleportation of a Two-Particle State by Two Three-Particle General \(W\) States

abstract

A scheme for teleporting an unknown two-particle state is proposed when two general \(W\) states are utilized as quantum channels. In this scheme, besides the sender’s Bell state measurements, the recipient need introduce an auxiliary particle, perform Von Neumann measurements and carry out appropriate unitary transformation. Finally, the recipient can realize teleportation with different probabilities of successful teleportaion by selecting different particles to recover the original state. In order to gain the biggest probability of successful teleportation, it is useful to select proper particles to reconstruct the state to be teleported.


Inverse Problem of Variational Calculus for Nonlinear Evolution Equations

abstract

We couple a nonlinear evolution equation with an associated one and derive the action principle. This allows us to write the Lagrangian density of the system in terms of the original field variables rather than Casimir potentials. We find that the corresponding Hamiltonian density provides a natural basis to recast the pair of equations in the canonical form. Amongst the case studies presented the KdV and modified KdV pairs exhibit bi-Hamiltonian structure and allow one to realize the associated fields in physical terms.


Matter Collineations of Static Spacetimes with Maximal Symmetric Transverse Spaces

abstract

This paper is devoted to study the symmetries of the energy-momentum tensor for the static spacetimes with maximal symmetric transverse spaces. We solve matter collineation equations for the four main cases by taking one, two, three and four non-zero components of the vector \(\xi ^a\). For one component non-zero, we obtain only one matter collineation for the non-degenerate case and for two components non-zero, the non-degenerate case yields maximum three matter collineations. When we take three components non-zero, we obtain three, four and five independent matter collineations for the non-degenerate and for the degenerate cases respectively. This case generalizes the degenerate case of the static spherically symmetric spacetimes. The last case (when all the four components are non-zero) provides the generalization of the non-degenerate case of the static spherically symmetric spacetimes. This gives either four, five, six, seven or ten independent matter collineations in which four are the usual Killing vectors and rest are the proper matter collineations. It is mentioned here that we obtain different constraint equations which, on solving, may provide some new exact solutions of the Einstein field equations.


Lepton Flavor Violating \(Z\rightarrow l_1^+ l_2^-\) Decays with the Localized New Higgs Doublet in the Extra Dimension

abstract

We predict the branching ratios of \(Z\rightarrow e^{\pm } \mu ^{\pm }\), \(Z\rightarrow e^{\pm } \tau ^{\pm }\) and \(Z\rightarrow \mu ^{\pm } \tau ^{\pm }\) decays in the framework of the 2HDM with the inclusion of one and two extra dimensions, by considering that the new Higgs doublet is localized in the extra dimension with a Gaussian profile. We observe that their BRs are at the order of the magnitude of \(10^{-10}\), \(10^{-8}\) and \(10^{-5}\) with the inclusion of a single extra dimension, in the given range of the free parameters. These numerical values are slightly suppressed in the case that the localization points of new Higgs scalars are different than origin.


Space, Phase Space and Quantum Numbers of Elementary Particles

abstract

We recall the arguments that there should be a close connection between the properties of elementary particles and the arena used for the description of macroscopic processes, and argue that a natural choice for this arena is provided by nonrelativistic phase space with momentum and position being independent variables. Accepting standard commutation relations for these variables, and adopting \({\mathbf x}^2+{\mathbf p}^2\) as an invariant, we linearise the latter á la Dirac. Phase space U(1) \(\otimes \) SU(3) symmetry is then represented in the relevant Clifford algebra. Within this algebra, the eigenvalues of the U(1) generator are \(\pm (+1\)/\(3,+1\)/\(3,+1\)/\(3,-1)\), characteristic of weak hypercharge \(Y\) for three coloured quarks and one lepton. The total U(1) generator contains contributions from the phase space and the Clifford algebra, and leads to a relation, which we propose to identify with the Gell-Mann–Nishijima–Glashow formula \(Q=I_3+Y\)/\(2\).


A Remark on Vector Meson Dominance, Universality and the Pion Form Factor

abstract

In this paper, we address the universality problem in the mass-mixing representation of vector meson dominance. First, we stress the importance of using physical (mass eigenstate) fields in order to get the correct \(q^2\) dependence of the pion form factor. Then we show that, when a direct coupling of the (proto-)photon to the pions is included, it is not necessary to invoke universality. Our method is similar to the delocalization idea in some deconstruction theories.


all authors

J. Lagoda, D. Kielczewska, M. Posiadala, R. Sulej, K. Zaremba, T. Kozlowski, K. Kurek, P. Mijakowski, P. Przewlocki, E. Rondio, J. Stepaniak, M. Szeptycka

Polarization Effects in tau Production by Neutrinos

abstract

A direct proof of the existence of \(\nu _\mu \rightarrow \nu _\tau \) oscillations is important. This proof can be obtained by an observation of the production of taons in charge current reactions \(\nu _\tau + N \rightarrow \tau + X\). The influence of \(\tau \) polarization on the characteristics of the CC events and on the efficiency of their selection is discussed. The neural network method is used to select \(\tau \) leptons produced in \(\nu _\tau \) interactions.


LHC and VLHC Based \(ep\) Colliders: \(e\)-Linac versus \(e\)-Ring

abstract

Linac-ring analogues of the LHC and VLHC based standard type \(ep\) collider proposals are discussed. It is shown that sufficiently high luminosities can be obtained with TESLA like linacs, whereas essential modifications are required for CLIC technology. The physics search potential of proposed ep colliders is demonstrated using pair production of heavy quarks as an example.


Density Dependent Meson Nucleon Couplings for Nuclear Matter and Finite Nuclei

abstract

The medium dependence of nuclear interactions is described by an effective Lagrangian characterized by density dependent meson nucleon couplings. The density dependence of the coupling parameters of the \(\sigma \), \(\omega \), \(\delta \), and \(\rho \) mesons is deduced by reproducing the nucleon self-energy resulting from the relativistic Brueckner–Hartree–Fock approach at each density for symmetric and asymmetric nuclear matter. The inclusion of the density dependent isovector mesons couplings, \(\delta \) and \(\rho \), affects the density and charge distributions of finite nuclei. The results are discussed and compared with experimental data and with results from similar approaches.


The Study of Fusion of Different Isotopes/Isotones Leading to the Same Compound Nucleus

abstract

We present the fusion of series of reactions of isotopes/isotones leading to the same compound nucleus. This is achieved by transferring either neutrons or protons from one to the other colliding nucleus. Our findings for the normalized barrier heights, positions as well as fusion cross-sections suggest that such fusion of transfer reactions can be parameterized in terms of an asymmetry power law with power factor close to two. This power factor is nearly the same as has been reported for the asymmetric term in mass formula.


all authors

J. Golak, R. Skibiński, H. Witała, W. Glöckle, A. Nogga, H. Kamada

Lorentz Boosted Nucleon–Nucleon Potential Applied to the \(\vec {^3{\rm He}} ({\vec e},e' p)pn\) and \(\vec {^3{\rm He}} ({\vec e},e' n)pp\) Reactions

abstract

We formulate an approximate relativistic framework for an analysis of the \( \vec {^3{\rm He}} ({\vec e},e' p)pn\) and \( \vec {^3{\rm He}} ({\vec e},e' n)pp\) reactions. Restricting the rescattering series to one term linear in the two-nucleon (\(2N\)) \(t\)-matrix we incorporate various relativistic features when calculating a nuclear current matrix element. These relativistic ingredients encompass the relativistic \(^3\)He wave function based on the concept of the Lorentz boosted nucleon–nucleon potential together with the boosted \(2N\) \(t\)-matrix, relativistic kinematics and relativistic single-nucleon current operator. This allows us to estimate the magnitude of certain relativistic effects not included in the standard nonrelativistic approach. A more complete inclusion of relativity would require that the current operator obeys the covariance equations and the final three-nucleon (\(3N\)) scattering state with complete final state interactions (FSI) should be properly boosted. We provide some discussion on those issues.


Wave Functions of Linear Systems

abstract

Complete analysis of quantum wave functions of linear systems in an arbitrary number of dimensions is given. It is shown how one can construct a complete set of stationary quantum states of an arbitrary linear system from purely classical arguments. This construction is possible because for linear systems classical dynamics carries the whole information about quantum dynamics.


Square Lattice Site Percolation Thresholds for Complex Neighbourhoods

abstract

In this paper we compute the square lattice random sites percolation thresholds in case when sites from the 4-th and the 5-th coordination shells are included for neighbourhood. The obtained results support earlier claims, that (a) the coordination number and the space dimension are insufficient for building universal formulae for percolation thresholds and (b) that percolation threshold may not decrease monotonically with lattice site coordination number.


Dynamics of the Model of the Caenorhabditis Elegans Neural Network

abstract

The model of the neural network of nematode worm C. elegans resulting from the biological investigations and published in the literature, is proposed. In the model artificial neurons \(S_{i}\in (-1,1)\) are connected in the same way as in the C. elegans neural network. The dynamics of this network is investigated numerically for the case of simple external simulation, using the methods developed for the nonlinear systems. In the computations a number of different attractors, e.g. point, quasiperiodic and chaotic, as well as the range of their occurrence, were found. These properties are similar to the dynamical properties of a simple one dimensional neural network with comparable number of neurons investigated earlier.


Spin Connection Resonance in Gravitational General Relativity

abstract

The equations of gravitational general relativity are developed with Cartan geometry using the second Cartan structure equation and the second Bianchi identity. These two equations combined result in a second order differential equation with resonant solutions. At resonance the force due to gravity is greatly amplified. When expressed in vector notation, one of the equations obtained from the Cartan geometry reduces to the Newton inverse square law. It is shown that the latter is always valid in the off resonance condition, but at resonance, the force due to gravity is greatly amplified even in the Newtonian limit. This is a direct consequence of Cartan geometry. The latter reduces to Riemann geometry when the Cartan torsion vanishes and when the spin connection becomes equivalent to the Christoffel connection.


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