The Jacobi identity for Dirac-like brackets

For redundant second-class constraints the Dirac brackets cannot be defined and new brackets must be introduced. We prove here that the Jacobi identity for the new brackets must hold on the surface of the second-class constraints. In order to illustrate our proof we work out explicitly the cases of a fractional spin particle in 2 + 1 dimensions and the original Brink-Schwarz massless superparticle in D = 10 dimensions in a Lorentz-covariant constraints separation.

Confinement of neutral fermions by a pseudoscalar double-step potential in 1+1 dimensions

The problem of confinement of neutral fermions in two-dimensional space-time is approached with a pseudoscalar double-step potential in the Dirac equation. Bound-state solutions are obtained when the coupling is of sufficient intensity. The confinement is made plausible by arguments based on effective mass and anomalous magnetic interaction. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Dirac-like monopoles in three dimensions and their possible influences on the dynamics of particles

Dirac-like monopoles are studied in three-dimensional Abelian Maxwell and Maxwell-Chern-Simons models. Their scalar nature is highlighted and discussed through a dimensional reduction of four-dimensional electrodynamics with electric and magnetic sources. Some general properties and similarities whether considered in Minkowski or Euclidean space are mentioned. However, by virtue of the structure of the space-time in which they are studied, a number of differences among them occur. Furthermore, we pay attention to some consequences of these objects when they act upon the usual particles. Among other subjects, special attention is given to the study of a Lorentz-violating nonminimal coupling between neutral fermions and the field generated by a monopole alone. In addition, an analogue of the Aharonov-Casher effect is discussed in this framework.

Scattering of neutral fermions by a pseudoscalar potential step in two-dimensional spacetime

The problem of scattering of neutral fermions in two-dimensional spacetime is approached with a pseudoscalar potential step in the Dirac equation. Some unexpected aspects of the solutions beyond the absence of Klein's paradox are presented. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength. Added plausibility for the existence of bound-state solutions in a pseudoscalar double-step potential found in a recent Letter is given. (C) 2003 Elsevier B.V. B.V. All rights reserved.

Bound states by a pseudoscalar Coulomb potential in one-plus-one dimensions

The Dirac equation is solved for a pseudoscalar Coulomb potential in a two-dimensional world. An infinite sequence of bounded solutions are obtained. These results are in sharp contrast with those ones obtained in 3 + 1 dimensions where no bound-state solutions are found. Next the general two-dimensional problem for pseudoscalar power-law potentials is addressed consenting us to conclude that a nonsingular potential leads to bounded solutions. The behaviour of the upper and lower components of the Dirac spinor for a confining linear potential nonconserving- as well as conserving-parity, even if the potential is unbounded from below, is discussed in some detail. (C) 2003 Elsevier B.V. All rights reserved.

The peremptory influence of a uniform background for trapping neutral fermions with an inversely linear potential

The problem of neutral fermions subject to an inversely linear potential is revisited. It is shown that an infinite set of bound-state solutions can be found on the condition that the fermion is embedded in an additional uniform background potential. An apparent paradox concerning the uncertainty principle is solved by introducing the concept of effective Compton wavelength.

Bounded solutions for nonconserving-parity pseudoscalar potentials

The Dirac equation is analyzed for nonconserving-parity pseudoscalar radial potentials in 3+1 dimensions. It is shown that despite the nonconservation of parity this general problem can be reduced to a Sturm-Liouville problem of nonrelativistic fermions in spherically symmetric effective potentials. The searching for bounded solutions is done for the power-law and Yukawa potentials. The use of the methodology of effective potentials allow us to conclude that the existence of bound-state solutions depends whether the potential leads to a definite effective potential-well structure or to an effective potential less singular than -1/4r(2).

Bounded solutions of neutral fermions with a screened Coulomb potential

The intrinsically relativistic problem of a fermion subject to a pseudoscalar screened Coulomb plus a uniform background potential in two-dimensional space-time is mapped into a Sturm-Liouville. This mapping gives rise to an effective Morse-like potential and exact bounded solutions are found. It is shown that the uniform background potential determinates the number of bound-state solutions. The behaviour of the eigenenergies as well as of the upper and lower components of the Dirac spinor corresponding to bounded solutions is discussed in detail and some unusual results are revealed. An apparent paradox concerning the uncertainty principle is solved by recurring to the concepts of effective mass and effective Compton wavelength. (c) 2005 Elsevier B.V. All rights reserved.

Relating pseudospin and spin symmetries through charge conjugation and chiral transformations: the case of the relativistic harmonic oscillator

We solve the generalized relativistic harmonic oscillator in 1+1 dimensions, i.e., including a linear pseudoscalar potential and quadratic scalar and vector potentials which have equal or opposite signs. We consider positive and negative quadratic potentials and discuss in detail their bound-state solutions for fermions and antifermions. The main features of these bound states are the same as the ones of the generalized three-dimensional relativistic harmonic oscillator bound states. The solutions found for zero pseudoscalar potential are related to the spin and pseudospin symmetry of the Dirac equation in 3+1 dimensions. We show how the charge conjugation and gamma(5) chiral transformations relate the several spectra obtained and find that for massless particles the spin and pseudospin symmetry-related problems have the same spectrum but different spinor solutions. Finally, we establish a relation of the solutions found with single-particle states of nuclei described by relativistic mean-field theories with scalar, vector, and isoscalar tensor interactions and discuss the conditions in which one may have both nucleon and antinucleon bound states.

Confinement of fermions by mixed vector-scalar linear potentials in two-dimensional space-time

The problem of confinement of fermions in 1 + 1 dimensions is approached with a linear potential in the Dirac equation by considering a mixing of Lorentz vector and scalar couplings. Analytical bound-states solutions are obtained when the scalar coupling is of sufficient intensity compared to the vector coupling. (C) 2002 Elsevier B.V. B.V. All rights reserved.

Bound states of the Duffin-Kemmer-Petiau equation with a mixed minimal-nonminimal vector cusp potential

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Comment on Solutions of the Duffin-Kemmer-Petiau equation for a pseudoscalar potential step in (1+1) dimensions

It is shown that the paper Solutions of the Duffin-Kemmer-Petiau equation for a pseudoscalar potential step in (1+1) dimensions by Abdelmalek Boumali has a number of misconceptions

Exotic dark spinor fields

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Heaviside generalized functions and shock waves for a Burger kind equation

The purpose of the work is to study the existence and nonexistence of shock wave solutions for the Burger equations. The study is developed in the context of Colombeau's theory of generalized functions (GFs). This study uses the equality in the strict sense and the weak equality of GFs. The shock wave solutions are given in terms of GFs that have the Heaviside function, in x and ( x, t) variables, as macroscopic aspect. This means that solutions are sought in the form of sequences of regularizations to the Heaviside function, in R-n and R-n x R, in the distributional limit sense.