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

摘要

We define a two-dirnensional 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 accommodates 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 a new point of view that can help us to give one more step toward the understanding of the spinor theory. 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 analyzing the bilinear covariant structures one by one. Published under license by AIP Publishing