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

TL;DR

This paper investigates the properties of restricted Inomata-McKinley spinors, showing they are necessarily of the first Lounesto class and lack exotic counterparts, with implications for understanding spacetime topology.

Contribution

It demonstrates that restricted Inomata-McKinley spinors are always first type Lounesto spinors and have no exotic counterparts, linking spinor classification to spacetime topology.

Findings

Restricted Inomata-McKinley spinors are first type Lounesto spinors.

These spinors lack exotic counterparts.

Results have implications for spacetime background 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.