arXiv subjects
Publications and source records attributed to R. J. Bueno Rogerio.
In this report we advance into a mapping procedure transmuting a single helicity spinor to a dual helicity spinor. Such a mathematical mechanism reveal us a class of spinor which fits into fourth class within Lounesto classification. The focus of the present manuscript is to expose the algebraic construction of flag-dipole spinors and briefly explore its underlying physical and mathematical contents.
In this theoretical communication we look towards understand the underlying phenomenology concerning the Elko spinors within VSR theory. The program to be accomplished here start when we define the eigenspinors of the charge conjugation operator as eigenstates of the helicity operator in the Cartesian coordinates system. This prescription is very useful in the sense of phenomenological point of view, so, we propose a set of Elko spinors ready to be computationally implemented. Regardless of, in order to show the application of given approach we impose to these spinors to be restrict to an axis, coincidentally the axis of locality, and then, using the proposed prescription, we search for physical amounts and physical processes by analysing the Yukawa and the self-interaction in such framework.
We define a two-dimensional space called the spinor-plane, where all spinors that can be decomposed in terms of Restricted Inomata-McKinley (RIM) spinors reside, and describe some of its properties. Some interesting results concerning the construction of RIM-decomposable spinors emerge when we look at them by means of their spinor-plane representations. We show that, in particular, this space accomodates a bijective linear map between mass-dimension-one and Dirac spinor fields. As a highlight result, the spinor-plane enables us to construct homotopic equivalence relations, revealing an algebraic-topological link between these spinors. In the end, we develop a simple method that provides the categorization of RIM-decomposable spinors in the Lounesto classification, working by means of spinor-plane coordinates, which avoids the often hard work of analising the bilinear covariant structures one by one.
In this communication we briefly report an unexpected theoretical discovery which emerge from the mapping of Elko mass-dimension-one spinors into single helicity spinors. Such procedure unveils a class of spinor which is classified as type-4 spinor field within Lounesto classification. In this paper we explore the underlying physical and mathematical contents of the type-4 spinor.
The RIM spinors (Restricted Inomata McKinley spinors) constitutes a very particular class of solutions of the non-linear Heisenberg equation. As a matter of fact, a free linear massive or even mass-less Dirac field can be decomposed into a combination of RIM spinors and such a procedure shows up to be useful to describe neutrino physics and neutrinos oscillation. In this paper we show that not only Dirac spinors but also mass-dimension-one spinors can be decomposed into a combination of non-linear Heisenberg spinors. In order to extend the analysis carried out, shedding light to explore mass-dimension-one fermions within Spinor Theory of Gravity scenario.
In this work we use momentum-space techniques to evaluate the propagator $G(x,x^{\prime})$ for a spin $1/2$ mass dimension one spinor field on a curved Friedmann-Robertson-Walker spacetime. As a consequence, we built the one-loop correction to the effective lagrangian in the coincidence limit. Going further we compute the effective lagrangian in the finite temperature regime. We arrive at interesting cosmological consequences, as time-dependent cosmological `constant', fully explaining the functional form of previous cosmological models.
In this present communication we provide a new derivation of the Dirac dual structure by employing a different approach from the originally proposed. Following a general and rigorous mathematical process to compute the dual structure, we investigate if is possible to break the existing "rigidity" in its primordial formulation. For this task, firstly, we look towards to understand the core of the Dirac spinors construction and then, we suggest to built an alternative dual structure for the Dirac spinor, which preserve an invariant norm under any $SL(2,\mathcal{C})$ transformation. Finally, we verify if the prominent physical contents are maintained or if it is affected by such construction.
A systematic study of the spinor representation by means of the fermionic physical space is accomplished and implemented. The spinor representation space is shown to be constrained by the Fierz-Pauli-Kofink identities among the spinor bilinear covariants. A robust geometric and topological structure can be manifested from the spinor space, wherein, for instance, the first and second homotopy groups play prominent roles on the underlying physical properties, associated to the fermionic fields.
In this paper we approach the issue of Clifford algebra basis deformation, allowing for bilinear covariants associated to Elko spinors which satisfy the Fierz-Pauli-Kofink identities. We present a complete analysis of covariance, taking into account the involved dual structure associated to Elko. Moreover, the possible generalizations to the recently presented new dual structure are performed.
Dirac spinors are important objects in the current literature, the algebraic structure presented in the text-books is a general method to write it, however, not unique. The purpose of the present work is to show an alternative approach to construct Dirac spinors, considering the interchange between the Lorentz representation space (1/2,0) and (0,1/2) made by the "Magic of Pauli matrices" and not by parity, as commonly it was thought. As it is well known, parity operator is related with the Dirac dynamics. The major focus is to establish the relation between Dirac dynamics with parity operator, the reverse path shown in L. D. Sperança (2014).
In this paper a mass dimension one fermionic sigma model, realized by the eigenspinors of the charge conjugation operator with dual helicity (Elko spinors), is developed. Such spinors are chosen as a specific realization of mass dimension one spinors, wherein the non-commutative fermionic feature is ruled by torsion. Moreover, we analyse Elko spinors as a source of matter in a background in expansion. Moreover, we analyse Elko spinors as a source of matter in a background in expansion and we have found that such kind of mass dimension one fermions can serve not only as dark matter but they also induce an effective cosmological constant.