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Thus, we describe some of its properties. Aiming an interesting application, we present a relation concerning Elko spinors and the neutrino physics via the Heisenberg non-linear theory by means of a bijective linear map between Elko spinors and the so-called Restricted Inomata-McKinley (RIM) spinors. With the appropriated bilinear forms at hands, we search for a real physical interpretation in order to achieve a deeper understanding of such spinor fields. Such protocol can be accomplished by taking precisely the right Elko dual structure during the construction of the bilinear forms related to these spinors.

Thus, by the aforementioned reasons, we develop a deformation of the Clifford algebra basis. As we shall see, such structures do not hold the right observance of the Fierz-Pauli-Kofink quadratic relations. We start the program exploring the physical information by evaluating the Elko bilinear forms, both within the proper orthochronous Lorentz subgroup as well as within the VSR theory. In the present essay we review the underlying physical information behind the first concrete example describing a mass dimension one fermion - namely Elko spinors. At the core of this framework lies the characterization, which we develop in detail, of the image of the spinor squaring map of an irreducible Clifford module Σ\documentclass M$. We develop a new framework for the study of generalized Killing spinors, where every generalized Killing spinor equation, possibly with constraints, can be formulated equivalently as a system of partial differential equations for a polyform satisfying algebraic relations in the Kähler–Atiyah bundle constructed by quantizing the exterior algebra bundle of the underlying manifold.