On the spinor representation

Hoff da Silva, J. M. (Departamento de Física e Química, Universidade Estadual Paulista, 0000 0001 2188 478X, Guaratinguetá, SP, Brazil) ; Villalobos, C. H. Coronado (Departamento de Física e Química, Universidade Estadual Paulista, 0000 0001 2188 478X, Guaratinguetá, SP, Brazil) (Instituto de Física, Universidade Federal Fluminense, 0000 0001 2184 6919, Av. Gal. Milton Tavares de Souza s/n, Gragoatá, 24210-346, Niterói, RJ, Brazil) ; da Rocha, Roldão (Centro de Matemática, Computação e Cognição, Universidade Federal do ABC-UFABC, 0000 0004 0643 8839, 09210-580, Santo André, Brazil) ; Rogerio, R. J. Bueno (Departamento de Física e Química, Universidade Estadual Paulista, 0000 0001 2188 478X, Guaratinguetá, SP, Brazil)

21 July 2017

Abstract: 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 the first and second homotopy groups play prominent roles on the underlying physical properties, associated to fermionic fields. The mapping that changes spinor fields classes is then exemplified, in an Einstein–Dirac system that provides the spacetime generated by a fermion.


Published in: EPJC 77 (2017) 487
Published by: Springer/Società Italiana di Fisica
DOI: 10.1140/epjc/s10052-017-5035-y
License: CC-BY-3.0



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