Eur. Phys. J. C (2020) 80: 228
https://doi.org/10.1140/epjc/s10052-020-7801-5

Regular Article - Theoretical Physics

On the generalized spinor classification: beyond the Lounesto’s classification

¹ Instituto Nacional de Pesquisas Espaciais (INPE), CEP 12227-010, São José dos Campos, SP, Brazil
² Instituto de Física e Química, Universidade Federal de Itajubá—IFQ (UNIFEI), Av. BPS 1303, CEP 37500-903, Itajubá, MG, Brazil
³ Departamento de Física e Química, Universidade Estadual Paulista (UNESP) Faculdade de Engenharia, Guaratinguetá, CEP 12516-410, Guaratinguetá, SP, Brazil

^* e-mail: rodolforogerio@unifei.edu.br

Received: 21 February 2020
Accepted: 2 March 2020
Published online: 10 March 2020

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 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 restrictions on the number of possible spinorial classes allowed in the classification. We also expose a subsidiary mathematical device—a slight modification on the Clifford algebra basis—which ensures real spinorial densities and holds the Fierz–Pauli–Kofink quadratic relations.