On the generalized spinor classification: Beyond the Lounesto's Classification

Abstract

In this paper we advance into a generalized spinor classification, based on the so-called Lounesto's classification. The program developed here is based on an existing freedom on the spinorial dual structures definition, which, in a certain simple physical and mathematical limit, allows us to recover the usual Lounesto's classification. The protocol to be accomplished here gives full consideration in the understanding of the underlying mathematical structure, in order to satisfy the quadratic algebraic relations known as Fierz-Pauli-Kofink identities, and also to provide physical observables. As we will see, such identities impose a given restriction on the number of possible spinorial classes allowed in the classification. We also expose a mathematical device known as \emph{Clifford's algebra deformation}, which ensures real spinorial densities and holds the Fierz-Pauli-Kofink quadratic relations.

arXiv comment9 pages, 0 figures

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Cited by in corpus (15)

• Constraints on mapping the Lounesto's Classes
• Regular spinors and fermionic fields
• Spin-half mass dimension one fermions and their higher-spin generalizations
• On Wigner Degeneracy in Elko theory: Hermiticity and Dark Matter
• Spinorial discrete symmetries and adjoint structures
• Revisiting Takahashi's inversion theorem in discrete symmetry-based dual frameworks
• Flag-dipole spinors: On the dual structure derivation and $\mathcal{C}$, $\mathcal{P}$ and $\mathcal{T}$ symmetries
• Subliminal aspects concerning the Lounesto's classification
• Singular spinors as expansion coefficients of local spin-half fermionic and bosonic fields: On the two-fold Wigner degeneracy
• Spinor Adjoints, Gauge Invariance and a new Road to Sterile Neutrinos
• Essential Fierz identities for a fermionic field
• A note on hidden classes in spinor classification
• Euler and Pontryagin currents of the Dirac operator
• Unraveling the Physical Meaning Behind Elko's Dual structure
• A Covariant Framework for Generalized Spinor Dual Structures