Causal phase in QED3

The operator S in Fock space which describes the scattering and particle production processes in an external time-dependent electromagnetic potential A can be constructed from the one-particle S-matrix up to a physical phase λ[A]. In this work we determine this phase for QED in (2 + 1) dimensions by means of causality and show that no ultraviolet divergences arise, in contrast to the usual formalism of QED3.

Description of inclusive meson spectra in e+e- annihilation reactions by a quark cascade model

We present a model to describe inclusive meson production in e+e- reactions based on a quark cascade approach whose formulation is put in terms of diffusion equations for three quark flavors (u, d, s). These equations are solved by using a formalism previously developed for the problem of the electromagnetic cascade generated in the atmosphere by cosmicray interactions. The obtained solutions are given in terms of a combination of power-law functions whose profiles are adequate to describe the characteristics observed in the inclusive spectrum of mesons.

Closed expressions for Lie algebra invariants and finite transformations

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements requires the use of projectors, whose coefficients are invariant polynomials. The detailed general forms of these projectors are given. Closed expressions for finite Lorentz transformations, both homogeneous and inhomogeneous, as well as for Galilei transformations, are found as examples.

Quantal information entropies for atoms

The polynomials occurring in the wave functions of hydrogenic excited states are found to present difficulties for a straightforward analytical approach to the study of associated information entropies. A method is suggested to deal with them. It is then applied to calculate the information entropy for the Jacobi polynomial. A model calculation is presented to examine the effect of screening on the entropy sum. It is seen that the sum does not depend on the choice of screening.

Algorithm for computing the propagator for higher derivative gravity theories

A simple algorithm for computing the propagator for higher derivative gravity theories based on the Barnes-Rivers operators is presented. The prescription is used, among other things, to obtain the propagator for quadratic gravity in an unconventional gauge. We also find the propagator for both gravity and quadratic gravity in an interesting gauge recently baptized the Einstein gauge [Hitzer and Dehnen, Int. J. Theor. Phys. 36 (1997), 559].

Vibrational-rotational structure of supersingular plus Coulomb potential A/r4 - Z/r*

The vibrational-rotational states of the supersingular plus Coulomb potential A/r4 - Z/r are variationally constructed using a nonorthogonal basis of atomic hydrogenic eigenfunctions modulated by an exponential factor exp(- α/r), ensuring the correct behavior in the vicinity of the supersingularity. The construction is carried out in two successive stages. The first stage is restricted to trial functions without radial nodes, leading to a variational optimization of the parameters of the basis for each value of the angular momentum. The second stage uses the complete basis to construct linear trial functions and to formulate the variational problem in terms of secular equations, yielding the successive vibrational and rotational states. Numerical results for the corresponding energy levels are presented for different combinations of the intensity parameters of the potential. © 2001 Plenum Publishing Corporation.

Merging higher derivative gravity and quantum mechanics

The most general quantum mechanical wave equation for a massive scalar particle in a metric generated by a spherically symmetric mass distribution is considered within the framework of higher derivative gravity (HDG). The exact effective Hamiltonian is constructed and the significance of the various terms is discussed using the linearized version of the above-mentioned theory. Not only does this analysis shed new light on the long standing problem of quantum gravity concerning the exact nature of the coupling between a massive scalar field and the background geometry, it also greatly improves our understanding of the role of HDG's coupling parameters in semiclassical calculations.

Conflict between the classical equivalence principle and quantum mechanics

As far as external gravitational fields described by Newton's theory are concerned, theory shows that there is an unavoidable conflict between the universality of free fall (Galileo's equivalence principle) and quantum mechanics - a result confirmed by experiment. Is this conflict due perhaps to the use of Newton's gravity, instead of general relativity, in the analysis of the external gravitational field? The response is negative. To show this we compute the low corrections to the cross-section for the scattering of different quantum particles by an external gravitational field, treated as an external field, in the framework of Einstein's linearized gravity. To first order the cross-sections are spin-dependent; if the calculations are pushed to the next order they become dependent upon energy as well. Therefore, the Galileo's equivalence and, consequently, the classical equivalence principle, is violated in both cases. We address these issues here.

On the bound-state spectrum of a nonrelativistic particle in the background of a short-ranged linear potential

The nonrelativistic problem of a particle immersed in a triangular potential well, set forth by N. A. Rao and B. A. Kagali, is revised. It is shown that these researchers misunderstood the full meaning of the potential and obtained a wrong quantization condition. By exploring the space inversion symmetry, this work presents the correct solution to this problem with potential applications in electronics in a simple and transparent way. © Electronic Journal of Theoretical Physics. All rights reserved.

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.

Heavy Mesons Spectroscopy

In this paper, Lippmann-Schwinger equation is solved by using Martin and Cornel potentials to calculate bc̄ energy levels. The results for some energy levels which are not observable, such as those of tt̄ in its short half-life are also predicted. Our calculated energy levels are in good agreement with results of other groups. The stability interval for Yukawa-Linear potential is also studied by investigating the spectrum of eigenvalues. © 2013 Springer Science+Business Media New York.

Light front fermion model propagation

In this work we consider the propagation of two fermion fields interacting with each other by the exchange of intermediate scalar bosons in the light front. We obtain the corrections up to fourth order in the coupling constant using hierarchical equations in order to obtain the bound state equation (Bethe - Salpeter equation). © 2013 Chinese Physical Society and IOP Publishing Ltd.

Supersimetria e o modelo mínimo supersimétrico

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Hipercomplexos: um estudo da analicidade e da hiperperiodicidade de funções octoniônicas

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the long standing issue of an R phi(2) coupling between gravity and a massless free scalar field

Using 2-body trees on a flat space background, it is shown that the actions A[g, φ] = (Latin small letter esh) d4x√-g [(R/2K) + (1/2)(gμν ∂μφ∂νφ + λRφ2)] and Ā[ḡ, φ̄] = (Latin small letter esh) d4x√ - ḡ [(R̄/2k) + (1/2) ḡμν∂μφ̄∂ νφ] describe the same theory at the tree-level in this case. We also demonstrate the quantum equivalence (at one-loop) of the barred and unbarred systems for λ == -1/6 (conformal coupling).