https://doi.org/10.1140/epjc/s10052-017-5035-y
Regular Article - Theoretical Physics
On the spinor representation
1
Departamento de Física e Química, Universidade Estadual Paulista, Guaratinguetá, SP, Brazil
2
Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/n, Gragoatá, Niterói, RJ, 24210-346, Brazil
3
Centro de Matemática, Computação e Cognição, Universidade Federal do ABC-UFABC, Santo André, 09210-580, Brazil
* e-mail: hoff@feg.unesp.br
Received:
16
February
2017
Accepted:
30
June
2017
Published online:
21
July
2017
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.
© The Author(s), 2017
