Remarks on mass dimension one fermions: The underlying aspects, bilinear forms, Spinor Classification and RIM decomposition

TL;DR

This paper reviews the physical properties of mass dimension one fermions called Elko spinors, exploring their bilinear forms, algebraic structures, and potential connections to neutrino physics through RIM spinors.

Contribution

It develops a deformation of the Clifford algebra basis for Elko spinors and establishes a relation between Elko and RIM spinors, advancing understanding of their physical interpretation.

Findings

Elko bilinear forms do not satisfy Fierz-Pauli-Kofink relations.

A deformed Clifford algebra basis is constructed for Elko spinors.

A linear map relates Elko spinors to RIM spinors, with implications for neutrino physics.

Abstract

In the present essay we review the underlying physical information behind the first concrete example describing a mass dimension one fermion - namely Elko spinors. 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. As we shall see, such structures do not hold the right observance of the Fierz-Pauli-Kofink quadratic relations. Thus, by the aforementioned reasons, we develop a deformation of the Clifford algebra basis. Such protocol can be accomplished by taking precisely the right Elko dual structure during the construction of the bilinear forms related to these 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. 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. Thus, we describe some of its properties. Some interesting results concerning the construction of RIM-decomposable spinors emerge from such prescription.