Flag-dipole spinor fields in ESK gravities

Abstract

Anisotropic cosmological models with spinor and scalar fields and viscous fluid in presence of a Λ term: Qualitative solutions J. Math. Phys. 49, 112502 (2008) We consider the Riemann-Cartan geometry as a basis for the Einstein-Sciama-Kibble theory coupled to spinor fields: we focus on f(R) and conformal gravities, regarding the flag-dipole spinor fields, type-(4) spinor fields under the Lounesto classification. We study such theories in specific cases given, for instance, by cosmological scenarios: we find that in such background the Dirac equation admits solutions that are not Dirac spinor fields, but in fact the aforementioned flag-dipoles ones. These solutions are important from a theoretical perspective, as they evince that spinor fields are not necessarily determined by their dynamics, but also a discussion on their structural (algebraic) properties must be carried off. Furthermore, the phenomenological point of view is shown to be also relevant, since for isotropic Universes they circumvent the question whether spinor fields do undergo the Cosmological Principle. C 2013 AIP Publishing LLC. [http://dx

The Theory of Local Mass Dimension One Fermions of Spin One Half

“…The Brazilian-Italian group of Roldão da Rocha, Hoff da Silva, Bueno Rogerio, Cavalcanti, Bonora, Fabbri, Silva-Neto, Bernardini, J. G. Pereira, and Coronado Villalobos, besides examining such important topics as Hawking radiation of mass dimension one fermions [73], continue to develop mathematical physics underlying Elko [73][74][75][76][77][78][79][80][81][82][83][84][85][86][87][88][89]. Of these we draw particular attention to mass-dimension transmuting operators considered in [75,77].…”

Opening the Pandora’s box of quantum spinor fields

“…Regarding type-6 spinors, still J = 0 and K = 0, however, the flag S is zero, terming it a dipole spinor field. Flagdipole spinor fields were shown to be a legitimate solution of the Dirac field equation in a torsional setup [6][7][8], whereas Elko and Majorana uncharged spinor fields represent type-5 spinors, although a recent example of a charged flag-pole spinor has been shown to be a solution of the Dirac equation [9]. More physical important examples on the Lounesto classification can be found in Refs.…”

“…Analyzing spinor fields that satisfy the Dirac equation does not necessarily bring about any information on which class this spinor field does belong to in the Lounesto classification. In fact, although solutions of the Dirac equation have been found in the literature to occupy all the Lounesto spinor classes [6,9,10], they are far from encompassing all the spinors in each spinor class. Besides the Weyl, Majorana and Elko spinors, there are more types of spinors with unknown dynamics in the Lounesto classification.…”

“…(5, 6) yieldsZ a = Z a . In fact, the homogeneous parts of (6) correspond to the bilinear covariants of some spinor [1]. Let us calculate, thus, Eq.…”

“…Although the spinors in (10) and (13) could be imposed to be in the same Lounesto's spinor class (4a-4f), there is no reason, a priori, to preclude the possibility that the spinors ψ 1 and ψ 2 are not in the same spinor class. In fact, the Dirac equation has solutions beyond the well-known textbook eigenspinors of the parity operator in the class 1 of the Lounesto classification, further encoding also flagdipole type-4 [6] and flag-pole type-5 [9] spinor solutions of the Dirac equation. Besides, one considers, as usual, anticommutators among creation/annihilation operators…”