ELKO Spinor Fields: Lagrangians for Gravity derived from Supergravity

Dual-helicity eigenspinors of the charge conjugation operator (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. Using the mapping from ELKO spinor fields to the three classes Dirac spinor fields, it is shown that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), as the prime Lagrangian for supergravity. The Holst action is related to the Ashtekar's quantum gravity formulation. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. Furthermore we consider the necessary and sufficient conditions to map Dirac spinor fields (DSFs) to ELKO, in order to naturally extend the Standard Model to spinor fields possessing mass dimension one. As ELKO is a prime candidate to describe dark matter and can be obtained from the DSFs, via a mapping explicitly constructed that does not preserve spinor field classes, we prove that in particular the Einstein-Hilbert, Einstein-Palatini, and Holst actions can be derived from the QSL, as a fundamental Lagrangian for supergravity, via ELKO spinor fields. The geometric meaning of the mass dimension-transmuting operator - leading ELKO Lagrangian into the Dirac Lagrangian - is also pointed out, together with its relationship to the instanton Hopf fibration.Comment: 11 pages, RevTeX, accepted for publication in Int.J.Geom.Meth.Mod.Phys. (2009

The quadratic spinor Lagrangian, axial torsion current, and generalizations

We show that the Einstein-Hilbert, the Einstein-Palatini, and the Holst actions can be derived from the Quadratic Spinor Lagrangian (QSL), when the three classes of Dirac spinor fields, under Lounesto spinor field classification, are considered. To each one of these classes, there corresponds a unique kind of action for a covariant gravity theory. In other words, it is shown to exist a one-to-one correspondence between the three classes of non-equivalent solutions of the Dirac equation, and Einstein-Hilbert, Einstein-Palatini, and Holst actions. Furthermore, it arises naturally, from Lounesto spinor field classification, that any other class of spinor field (Weyl, Majorana, flagpole, or flag-dipole spinor fields) yields a trivial (zero) QSL, up to a boundary term. To investigate this boundary term we do not impose any constraint on the Dirac spinor field, and consequently we obtain new terms in the boundary component of the QSL. In the particular case of a teleparallel connection, an axial torsion 1-form current density is obtained. New terms are also obtained in the corresponding Hamiltonian formalism. We then discuss how these new terms could shed new light on more general investigations.Comment: 9 pages, RevTeX, to be published in Int.J.Mod.Phys.D (2007

Hidden Consequence of Active Local Lorentz Invariance

In this paper we investigate a hidden consequence of the hypothesis that Lagrangians and field equations must be invariant under active local Lorentz transformations. We show that this hypothesis implies in an equivalence between spacetime structures with several curvature and torsion possibilities.Comment: Some misprints appearing in the published version have been correcte

Risco e Vulnerabilidade Social feminina

Este trabalho visa refletir sobre o conceito de vulnerabilidade social associada à ideia de Sociedade de Risco desenvolvida por Ulrich Beck e Anthony Giddens. Dentro desta perspectiva procura identificar e discutir sobre quem são os grupos vulneráveis em nossa sociedade através de um corte a partir de duas categorias de análise, classe e gênero. Compreendendo assim, que dentro de uma sociedade que se organiza a partir de um modo de vida capitalista, as mulheres pobres estão em risco extremo

β-Arrestin-2 regulates the development of allergic asthma

Asthma is a chronic inflammatory disorder of the airways that is coordinated by Th2 cells in both human asthmatics and animal models of allergic asthma. Migration of Th2 cells to the lung is key to their inflammatory function and is regulated in large part by chemokine receptors, members of the seven-membrane-spanning receptor family. It has been reported recently that T cells lacking β-arrestin-2, a G protein-coupled receptor regulatory protein, demonstrate impaired migration in vitro. Here we show that allergen-sensitized mice having a targeted deletion of the β-arrestin-2 gene do not accumulate T lymphocytes in their airways, nor do they demonstrate other physiological and inflammatory features characteristic of asthma. In contrast, the airway inflammatory response to LPS, an event not coordinated by Th2 cells, is fully functional in mice lacking β-arrestin-2. β-arrestin-2-deficient mice demonstrate OVA-specific IgE responses, but have defective macrophage-derived chemokine-mediated CD4+ T cell migration to the lung. This report provides the first evidence that β-arrestin-2 is required for the manifestation of allergic asthma. Because β-arrestin-2 regulates the development of allergic inflammation at a proximal step in the inflammatory cascade, novel therapies focused on this protein may prove useful in the treatment of asthma

Reply to Itin, Obukhov and Hehl paper "An Electric Charge has no Screw Sense - A Comment on the Twist-Free Formulation of Electrodynamics by da Rocha & Rodrigues"

In this note we briefly comment a paper by Itin, Obukhov and Hehl criticising our previous paper. We show that all remarks by our critics are ill conceived or irrelevant to our approach and moreover we provide some pertinent new comments to their critical paper, with the aim to clarify even more our view on the subject.Comment: This paper is a reply to arXiv:0911.5175 [physics.class-ph] which made some criticisms on our paper "Pair and Impar, Even and Odd Form Fields and Electromagnetism" arXiv:0811.1713 [math-ph] to appear in Annalen der Physik. A short version of our reply will also appear in Annalen de Physi