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

• Autor(a) principal: Beghetto, D. [UNESP]
• Data de Publicação: 2019
• Outros Autores: Rogerio, R. J. Bueno [UNESP], Villalobos, C. H. Coronado
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Institucional da UNESP
• Texto Completo: http://dx.doi.org/10.1063/1.5086440; http://hdl.handle.net/11449/188954

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 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.