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 massless) Dirac fields are well known to be represented as a combination of Inomata-McKinley spinors. More recently, a subclass of Inomata-McKinley spinors was 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 these type-one subclass spinors have not an exotic counterpart. Finally, implications of these results are discussed, regarding the understanding of the spacetime background topology.