Elko Spinor Fields and Massive Magnetic Like Monopoles

TL;DR

This paper revisits Elko spinor fields, demonstrating they have mass dimension 3/2, and explores their potential as dark matter candidates due to their magnetic-like charges and weak interactions with electromagnetic fields.

Contribution

It establishes that Elko fields have mass dimension 3/2, derives their equations from a Lagrangian, and proposes their role in forming dark matter-like condensates with magnetic charges.

Findings

Elko fields have mass dimension 3/2, not 1.

K and M fields are Clifford-valued, neutral, and carry magnetic-like charges.

Potential role of Elko fields as dark matter candidates.

Abstract

In this paper we recall that by construction Elko spinor fields of {\lambda} and {\rho} types satisfy a coupled system of first order partial differential equations (csfopde) that once interacted leads to Klein-Gordon equations for the {\lambda} and {\rho} type fields. Since the csfopde is the basic one and since the Klein-Gordon equations for {\lambda} and {\rho} possess solutions that are not solutions of the csfopde for {\lambda} and {\rho} we infer that it is legitimate to attribute to those fields mass dimension 3/2 (as is the case of Dirac spinor fields) and not mass dimension 1 as previously suggested in recent literature (see list of references). A proof of this fact is offered by deriving the csfopde for the {\lambda} and {\rho} from a Lagrangian where these fields have indeed mass dimension 3/2. Taking seriously the view that Elko spinor fields due to its special properties given by their bilinear invariants may be the description of some kind of particles in the real world a question then arises: what is the physical meaning of these fields? Here we proposed that the fields {\lambda} and {\rho} serve the purpose of building the fields K and M (see Eq.(38))which are Clifford valued multiform fields representing spinor fields in the Clifford bundle. They are electrically neutral and do not couple to the electromagnetic field but carry magnetic like charges which permit them to couple to a su(2) valued potential. If the potential is of short range the particles described by the K and M fields may be interacting and forming condensates of zero spin particles analogous to dark matter, in the sense that they do not couple with the electromagnetic field (generated by charged particles) and are thus invisible. We calculate the correct propagators for the K and M fields. We discuss also the main difference between Elko and Majorana spinor fields.