The (restricted) Inomata-McKinley spinor representation and the underlying topology

Abstract

The so called Inomata-McKinley spinors are a particular solution of the non-linear Heisenberg equation. In fact, free linear massive (or mass-less) Dirac fields are well known to be represented as a combination of Inomata-McKinley spinors. More recently, a subclass of Inomata-McKinley spinors were used to describe neutrino physics. In this paper we show that Dirac spinors undergoing this restricted Inomata-McKinley decomposition are necessarily of the first type, according to the Lounesto classification. Moreover, we also show that this type one subclass spinors has not an exotic counterpart. Finally, implications of these results are discussed, regarding the understanding of the spacetime background topology.

arXiv comment7 pages, to appear in EPL

References in corpus (3)

• Exotic Dark Spinor Fields
• On the Spinor Representation
• Constructing Dirac linear fermions in terms of non-linear Heisenberg spinors

Cited by in corpus (7)

• Constraints on mapping the Lounesto's Classes
• The Heisenberg spinor field classification and its interplay with the Lounesto's classification
• The Restricted Inomata-McKinley spinor-plane, homotopic deformations and the Lounesto classification
• Emergent spinor fields from exotic spin structures
• Spinorial structures, discrete symmetries and some consequences
• Additional fermionic fields onto parallelizable 7-spheres
• Foundational aspects of spinor structures and exotic spinors