Exact solutions of the dirac equation for modified coulombic potentials

Exact solutions are found for the Dirac equation for a combination of Lorentz scalar and vector Coulombic potentials with additional non-Coulombic parts. An appropriate linear combination of Lorentz scalar and vector non-Coulombic potentials, with the scalar part dominating, can be chosen to give exact analytic Dirac wave functions. The method works for the ground state or for the lowest orbital state with l = j - 1/2 , for any j.

Numerical study of the coupled time-dependent Gross-Pitaevskii equation: Application to Bose-Einstein condensation

The Bose-Einstein condensate of several types of trapped bosons at ultralow temperature was described using the coupled time dependent Gross-Pitaevskii equation. Both the stationary and time evolution problems were analyzed using this approach. The ground state stationary wave functions were found to be sharply peaked near the origin for attractive interatomic interaction for larger nonlinearity while for a repulsive interatomic interaction the wave function extends over a larger region of space.

Renormalization of the ladder light-front Bethe-Salpeter equation in the Yukawa model

The reduction of the two-fermion Bethe-Salpeter equation in the framework of light-front dynamics is studied for the Yukawa model. It yields auxiliary three-dimensional quantities for the transition matrix and the bound state. The arising effective interaction can be perturbatively expanded in powers of the coupling constant gs allowing a defined number of boson exchanges; it is divergent and needs renormalization; it also includes the instantaneous term of the Dirac propagator. One possible solution of the renormalization problem of the boson exchanges is shown to be provided by expanding the effective interaction beyond single boson exchange. The effective interaction in ladder approximation up to order g4 s is discussed in detail. It is shown that the effective interaction naturally yields the box counterterm required to be introduced ad hoc previously. The covariant results of the Bethe-Salpeter equation can be recovered from the corresponding auxiliary three-dimensional quantities.

Measurement of the pp(-)-> W gamma plus X cross section at root s=1.96 TeV and WW gamma anomalous coupling limits

The WWγ triple gauge boson coupling parameters are studied using pp̄rarr; νγ+X(=e,μ) events at s=1.96 TeV. The data were collected with the D0 detector from an integrated luminosity of 162pb-1 delivered by the Fermilab Tevatron Collider. The cross section times branching fraction for pp̄→W(γ)+X→ νγ+X with ETγ>8 GeV and ΔR γ> 0.7 is 14.8±1.6(stat)±1.0(syst) ±1.0(lum)pb. The one-dimensional 95% confidence level limits on anomalous couplings are -0.88<Δκγ<0.96 and -0. 20<λγ<0.20. © 2005 The American Physical Society.

The Dirac-Hestenes equation for spherical symmetric potentials in the spherical and Cartesian gauges

In this paper, using the apparatus of the Clifford bundle formalism, we show how straightforwardly solve in Minkowski space-time the Dirac-Hestenes equation - which is an appropriate representative in the Clifford bundle of differential forms of the usual Dirac equation - by separation of variables for the case of a potential having spherical symmetry in the Cartesian and spherical gauges. We show that, contrary to what is expected at a first sight, the solution of the Dirac-Hestenes equation in both gauges has exactly the same mathematical difficulty. © World Scientific Publishing Company.

Gluon mass generation in the PT-BFM scheme

In this article we study the general structure and special properties of the Schwinger-Dyson equation for the gluon propagator constructed with the pinch technique, together with the question of how to obtain infrared finite solutions, associated with the generation of an effective gluon mass. Exploiting the known all-order correspondence between the pinch technique and the background field method, we demonstrate that, contrary to the standard formulation, the non-perturbative gluon self-energy is transverse order-by-order in the dressed loop expansion, and separately for gluonic and ghost contributions. We next present a comprehensive review of several subtle issues relevant to the search of infrared finite solutions, paying particular attention to the role of the seagull graph in enforcing transversality, the necessity of introducing massless poles in the three-gluon vertex, and the incorporation of the correct renormalization group properties. In addition, we present a method for regulating the seagull-type contributions based on dimensional regularization; its applicability depends crucially on the asymptotic behavior of the solutions in the deep ultraviolet, and in particular on the anomalous dimension of the dynamically generated gluon mass. A linearized version of the truncated Schwinger-Dyson equation is derived, using a vertex that satisfies the required Ward identity and contains massless poles belonging to different Lorentz structures. The resulting integral equation is then solved numerically, the infrared and ultraviolet properties of the obtained solutions are examined in detail, and the allowed range for the effective gluon mass is determined. Various open questions and possible connections with different approaches in the literature are discussed. © SISSA 2006.

On a negative flow of the AKNS hierarchy and its relation to a two-component Camassa-Holm equation?

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Z gamma production and limits on anomalous ZZ gamma and Z gamma gamma couplings in pp collisions at root s=1.96 TeV

We present a study of eeγ and μμγ events using 1109 (1009) pb-1 of data in the electron (muon) channel, respectively. These data were collected with the DØ detector at the Fermilab Tevatron p over(p, ̄) collider at sqrt(s) = 1.96   TeV. Having observed 453 (515) candidates in the eeγ (μμγ) final state, we measure the Zγ production cross section for a photon with transverse energy ET > 7   GeV, separation between the photon and leptons Δ Rℓ γ > 0.7, and invariant mass of the di-lepton pair Mℓ ℓ > 30   GeV / c2, to be 4.96 ± 0.30 (stat . + syst .) ± 0.30 (lumi .)   pb, in agreement with the Standard Model prediction of 4.74 ± 0.22   pb. This is the most precise Zγ cross section measurement at a hadron collider. We set limits on anomalous trilinear Zγγ and ZZγ gauge boson couplings of - 0.085 < h30 γ < 0.084, - 0.0053 < h40 γ < 0.0054 and - 0.083 < h30 Z < 0.082, - 0.0053 < h40 Z < 0.0054 at the 95% C.L. for the form-factor scale Λ = 1.2   TeV.

First study of the radiation-amplitude zero in W gamma production and limits on anomalous WW gamma couplings at root s=1.96 TeV

We present results from a study of pp̄→Wγ+X events utilizing data corresponding to 0.7fb-1 of integrated luminosity at s=1.96TeV collected by the D0 detector at the Fermilab Tevatron Collider. We set limits on anomalous WWγ couplings at the 95% C.L. The one-dimensional 95% C.L. limits are 0.49<κγ<1.51 and -0.12<λγ<0.13. We make the first study of the charge-signed rapidity difference between the lepton and the photon and find it to be indicative of the standard model radiation-amplitude zero in the Wγ system. © 2008 The American Physical Society.

Antinucleon spectra in the Dirac equation with scalar and vector Wood-Saxon potentials

We analyze here the spin and pseudospin symmetry for the antinucleon spectra solving the Dirac equation with scalar and vector Wood-Saxon potentials. In relativistic nuclear mean field theories where these potentials have large magnitudes and opposite signs we show that contrary to the nucleon case where pseudospin interaction is never very small and cannot be treated perturbatively, for antinucleon systems this interaction is perturbative and an exact pseudospin symmetry is possible. This result manifests the relativistic nature of the nuclear pseudospin symmetry. © 2009 American Institute of Physics.

Darboux-Bäcklund transformations and rational solutions of the painlevé IV equation

Rational solutions of the Painlevé IV equation are constructed in the setting of pseudo-differential Lax formalism describing AKNS hierarchy subject to the additional non-isospectral Virasoro symmetry constraint. Convenient Wronskian representations for rational solutions are obtained by successive actions of the Darboux-Bäcklund transformations. ©2010 American Institute of Physics.

Stability of the null solution of the equation ẋ(t) = -a(t)x(t) + b(t)x([t])

The asymptotic stability of the null solution of the equation ẋ(t) = -a(t)x(t)+b(t)x([t]) with argument [t], where [t] designates the greatest integer function, is studied by means of dichotomic maps. © 2010 Academic Publications.

State Dependent Riccati Equation (SDRE) control method applied in cancellation of a parametric resonance in a magnetically levitated body

Here, a simplified dynamical model of a magnetically levitated body is considered. The origin of an inertial Cartesian reference frame is set at the pivot point of the pendulum on the levitated body in its static equilibrium state (ie, the gap between the magnet on the base and the magnet on the body, in this state). The governing equations of motion has been derived and the characteristic feature of the strategy is the exploitation of the nonlinear effect of the inertial force associated, with the motion of a pendulum-type vibration absorber driven, by an appropriate control torque [4]. In the present paper, we analyzed the nonlinear dynamics of problem, discussed the energy transfer between the main system and the pendulum in time, and developed State Dependent Riccati Equation (SDRE) control design to reducing the unstable oscillatory movement of the magnetically levitated body to a stable fixed point. The simulations results showed the effectiveness of the (SDRE) control design. Copyright © 2011 by ASME.

Geometrical wave equation and the cauchy-like theorem for octonions

Riemann surfaces, cohomology and homology groups, Cartan's spinors and triality, octonionic projective geometry, are all well supported by Complex Structures [1], [2], [3], [4]. Furthermore, in Theoretical Physics, mainly in General Relativity, Supersymmetry and Particle Physics, Complex Theory Plays a Key Role [5], [6], [7], [8]. In this context it is expected that generalizations of concepts and main results from the Classical Complex Theory, like conformal and quasiconformal mappings [9], [10] in both quaternionic and octonionic algebra, may be useful for other fields of research, as for graphical computing enviromment [11]. In this Note, following recent works by the autors [12], [13], the Cauchy Theorem will be extended for Octonions in an analogous way that it has recentely been made for quaternions [14]. Finally, will be given an octonionic treatment of the wave equation, which means a wave produced by a hyper-string with initial conditions similar to the one-dimensional case.

A simple derivation of the Lindblad equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)