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.
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In this work, what we call by a manifold with underlying trivial topology is a manifold M that has a trivial fundamental group π1(M) = 0. Otherwise, the manifold M will be said to have a non-trivial topology.
The fundamental field equations must be non-linear in order to represent interaction. The masses of the particles should be a consequence of this interaction.18
The authors choose to work in abstract only with the spinors since the physical content holds the same for all the other MDO spinors, one differing from the other only by a constant phase.
