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

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.

arXiv comment17 pages, 0 figures. To be published in Journal of Mathematical Physics. arXiv admin note: text overlap with arXiv:1803.00672

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• Hearing the shape of inequivalent spin structures and exotic Dirac operators
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