Non-standard Dirac adjoint spinor: The emergence of a new dual

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.Comment: 7 pages, 0 figure

Questing for Algebraic Mass Dimension One Spinor Fields

This work deals with new classes of spinors of mass dimension one in Minkowski spacetime. In order to accomplish it, the Lounesto classification scheme and the inversion theorem are going to be used. The algebraic framework shall be revisited by explicating the central point performed by the Fierz aggregate. Then the spinor classification is generalized in order to encompass the new mass dimension one spinors. The spinor operator is shown to play a prominent role to engender the new mass dimension one spinors, accordingly.Comment: 7 pages, final version to appear in Eur. Phys. J.

Type-4 spinors: transmuting from Elko to single-helicity spinors

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.Comment: 9 pages, 0 figure

Singular spinors as expansion coefficients of local spin-half fermionic and bosonic fields

By scrutinizing the singular sector of the Lounesto spinor classification, we investigate the correct definition of the expansion coefficient functions of local fermionic fields within a fully Lorentz covariant theory. As we can observe, a careful definition of the adjoint structure, directed towards local fields, maps singular spinors into class-2 according to a general spinor classification. Furthermore, we investigate all the necessary mathematical tools for constructing local fermionic and bosonic fields and provide insights into the physical implications for the other singular classes. Besides, we also show that incorporating \emph{Wigner degeneracy} maintains the rotational symmetry formalism working in general.Comment: 14 page

On the bilinear covariants associated to mass dimension one spinors

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.Comment: 9 pages, 0 figure

On the Spinor Representation

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.Comment: 16 page

Flag-dipole spinors: On the dual structure derivation and C\mathcal{C}, P\mathcal{P} and T\mathcal{T} symmetries

In this manuscript we report the flag-dipole spinors dual structure direct definition and analyze the properties behind the corresponding operator which generates such structure. This particular construction may be interesting for cosmological, phenomenological and mathematical physics applications. In addition, we analyse the behaviour of the flag-dipole spinors under action of discrete symmetries, facing an \emph{unconventional} property encoded on $(\mathcal{CPT})^2$.Comment: 8 pages, 0 figure