From Dirac Action to ELKO Action

TL;DR

This paper introduces a dynamical transformation linking Dirac and ELKO spinor fields, enabling the incorporation of dark matter candidates into the Standard Model through a mass dimension transmutation.

Contribution

It presents the first dynamical mapping between Dirac and ELKO spinors, extending the Standard Model to include dark matter fields via a mass dimension transmutation operator.

Findings

Defines a mass dimension-transmuting operator between Dirac and ELKO fields

Shows the operator as a composition of the Dirac operator and a non-unitary transformation

Demonstrates the potential to incorporate ELKO as dark matter into the Standard Model

Abstract

A fundamental action, representing a mass dimension-transmuting operator between Dirac and ELKO spinor fields, is performed on the Dirac Lagrangian, in order to lead it into the ELKO Lagrangian. Such a dynamical transformation can be seen as a natural extension of the Standard Model that incorporates dark matter fields. The action of the mass dimension-transmuting operator on a Dirac spinor field, that defines and introduces such a mapping, is shown to be a composition of the Dirac operator and the non-unitary transformation that maps Dirac spinor fields into ELKO spinor fields, defined in a previous paper. This paper gives allowance for ELKO, as a candidate to describe dark matter, to be incorporated in the Standard Model. It is intended to present for the first time, up to our knowledge, the dynamical character of a mapping between Dirac and ELKO spinor fields, transmuting the mass dimension of spin one-half fermionic fields from 3/2 to 1 and from 1 to 3/2.