Spin and pseudospin symmetries in the Dirac equation with central Coulomb potentials

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

On the symplectic two-form of gravity in terms of Dirac eigenvalues

The Dirac eigenvalues form a subset of observables of the Euclidean gravity. The symplectic two-form in the covariant phase space could be expressed, in principle, in terms of the Dirac eigenvalues. We discuss the existence of the formal solution of the equations defining the components of the symplectic form in this framework. (C) 2002 Published by Elsevier B.V. B.V.

Dirac's hole theory versus quantum field theory

Dirac's hole theory and quantum field theory are usually considered equivalent to each other. The equivalence, however, does not necessarily hold, as we discuss in terms of models of a certain type. We further suggest that the equivalence may fail in more general models. This problem is closely related to the validity of the Pauli principle in intermediate states of perturbation theory.

Lessons of spin and torsion: Reply to Consistent coupling to Dirac fields in teleparallelism

In reply to the criticism made by Mielke in the preceding Comment on our recent paper, we once again explicitly demonstrate the inconsistency of the coupling of a Dirac field to gravitation in the teleparallel equivalent of general relativity. Moreover, we stress that the mentioned inconsistency is generic for all sources with spin and is by no means restricted to the Dirac field. In this sense the SL(4,R)-covariant generalization of the spinor fields in the teleparallel gravity theory is irrelevant to the inconsistency problem.

Duality between coordinates and Dirac field

The duality between the Cartesian coordinates on the Minkowski space-time and the Dirac field is investigated. Two distinct possibilities to define this duality are shown to exist. In both cases, the equations satisfied by prepotentials are of second order. (C) 2000 Elsevier B.V. B.V. All rights reserved.

Kerr-Newman solution as a Dirac particle

For m(2) < a(2) + q(2), with m, a, and q respectively the source mass, angular momentum per unit mass, and electric charge, the Kerr-Newman (KN) solution of Einstein's equation reduces to a naked singularity of circular shape, enclosing a disk across which the metric components fail to be smooth. By considering the Hawking and Ellis extended interpretation of the KN spacetime, it is shown that, similarly to the electron-positron system, this solution presents four inequivalent classical states. Making use of Wheeler's idea of charge without charge, the topological structure of the extended KN spatial section is found to be highly non-trivial, leading thus to the existence of gravitational states with half-integral angular momentum. This property is corroborated by the fact that, under a rotation of the space coordinates, those inequivalent states transform into themselves only after a 4π rotation. As a consequence, it becomes possible to naturally represent them in a Lorentz spinor basis. The state vector representing the whole KN solution is then constructed, and its evolution is shown to be governed by the Dirac equation. The KN solution can thus be consistently interpreted as a model for the electron-positron system, in which the concepts of mass, charge and spin become connected with the spacetime geometry. Some phenomenological consequences of the model are explored.

From Dirac spinor fields to eigenspinoren des ladungskonjugationsoperators

Dual-helicity eigenspinors of the charge conjugation operator [eigenspinoren des ladungskonjugationsoperators (ELKO) spinor fields] belong-together with Majorana spinor fields-to a wider class of spinor fields, the so-called flagpole spinor fields, corresponding to the class (5), according to Lounesto spinor field classification based on the relations and values taken by their associated bilinear covariants. There exists only six such disjoint classes: the first three corresponding to Dirac spinor fields, and the other three, respectively, corresponding to flagpole, flag-dipole, and Weyl spinor fields. This paper is devoted to investigate and provide the necessary and sufficient conditions to map Dirac spinor fields to ELKO, in order to naturally extend the standard model to spinor fields possessing mass dimension 1. As ELKO is a prime candidate to describe dark matter, an adequate and necessary formalism is introduced and developed here, to better understand the algebraic, geometric, and physical properties of ELKO spinor fields, and their underlying relationship to Dirac spinor fields. (c) 2007 American Institute of Physics.

FROM DIRAC ACTION TO ELKO ACTION

A fundamental action, representing a mass dimension-transmuting operator between Dirac and ELKO spinor fields, is performed on the Dirac Lagrangian, in order to lead it into the ELKO Lagrangian. Such a dynamical transformation can be seen as a natural extension of the Standard Model that incorporates dark matter fields. The action of the mass dimension-transmuting operator on a Dirac spinor field, that de fines and introduces such a mapping, is shown to be a composition of the Dirac operator and the nonunitary transformation that maps Dirac spinor fields into ELKO spinor fields, de fined in J. Math. Phys. 4 8, 123517 (2007). This paper gives allowance for ELKO, as a candidate to describe dark matter, to be incorporated in the Standard Model. It is intended to present for the first time, up to our knowledge, the dynamical character of a mapping between Dirac and ELKO spinor fields, transmuting the mass dimension of spin one-half fermionic fields from 3/2 to 1 and from 1 to 3/2.

The Schrodinger and Pauli-Dirac Oscillators in Noncommutative Phase Space

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Green functions of the Dirac equation with magnetic-solenoid field

Various Green functions of the Dirac equation with a magnetic-solenoid field (the superposition of the Aharonov-Bohm field and a collinear uniform magnetic field) are constructed and studied. The problem is considered in 2+1 and 3+1 dimensions for the natural extension of the Dirac operator (the extension obtained from the solenoid regularization). Representations of the Green functions as proper time integrals are derived. The nonrelativistic limit is considered. For the sake of completeness the Green functions of the Klein-Gordon particles are constructed as well. (C) 2004 American Institute of Physics.

DIRAC CONFINEMENT BY A VARIATIONAL APPROACH

An analytical approximate method for the Dirac equation with confining power law scalar plus vector potentials, applicable to the problem of the relativistic quark confinement, is presented. The method consists in an improved version of a saddle-point variational approach and it is applied to the fundamental state of massless single quarks for some especial cases of physical interest. Our treatment emphasizes aspects such as the quantum-mechanical relativistic Virial theorem, the saddle-point character of the critical point of the expectation value of the total energy, as well as the Klein paradox and the behaviour of the saddle-point variational energies and wave functions.

LIMIT ON A HEAVY DIRAC NEUTRINO THROUGH OBLIQUE RADIATIVE-CORRECTIONS

We compute the one-loop oblique corrections in a typical model with neutrino masses due to the seesaw mechanism. We verify that a Dirac neutrino mass up to 178 GeV is still allowed by the experimental data.