The Restricted Inomata-McKinley spinor-plane, homotopic deformations and the Lounesto classification

TL;DR

This paper introduces a two-dimensional spinor-plane for RIM spinors, establishing a bijective map between different spinor types, and develops a topological classification method within the Lounesto framework, simplifying spinor categorization.

Contribution

It defines the spinor-plane for RIM spinors, constructs a bijective map between spinor fields, and introduces a topological approach to classify spinors in the Lounesto scheme.

Findings

The spinor-plane hosts a bijective linear map between mass-dimension-one and Dirac spinors.

Homotopic equivalence relations reveal algebraic-topological links between spinor types.

A new method categorizes RIM-decomposable spinors using spinor-plane coordinates, bypassing complex covariant analysis.

Abstract

We define a two-dimensional space called the spinor-plane, where all spinors that can be decomposed in terms of Restricted Inomata-McKinley (RIM) spinors reside, and describe some of its properties. Some interesting results concerning the construction of RIM-decomposable spinors emerge when we look at them by means of their spinor-plane representations. We show that, in particular, this space accomodates a bijective linear map between mass-dimension-one and Dirac spinor fields. As a highlight result, the spinor-plane enables us to construct homotopic equivalence relations, revealing an algebraic-topological link between these spinors. In the end, we develop a simple method that provides the categorization of RIM-decomposable spinors in the Lounesto classification, working by means of spinor-plane coordinates, which avoids the often hard work of analising the bilinear covariant structures one by one.