Elko and mass dimension one field of spin one half: causality and Fermi statistics

TL;DR

This paper reviews Elko spinors as extensions of Majorana spinors, demonstrating their unique properties such as causality, Fermi statistics, and mass dimension one, distinct from Dirac spinors.

Contribution

It clarifies the properties of Elko spinors, proving they cannot satisfy Dirac equations and establishing their causality and Fermi statistics within a quantum field framework.

Findings

Elko spinors do not satisfy Dirac equation

Elko fields are causal and obey Fermi statistics

Elko has mass dimension one

Abstract

We review how Elko arise as an extension of complex valued four-component Majorana spinors. This is followed by a discussion that constrains certain elements of phase freedom. A proof is reviewed that unambiguously establishes that Elko, and for that matter the indicated Majorana spinors, cannot satisfy Dirac equation. They, however do, as they must, satisfy spinorial Klein-Gordon equation. We then introduce a quantum field with Elko as its expansion coefficients and show that it is causal, satisfies Fermi statistics, and then refer to the existing literature to remind that its mass dimensionally is one. We conclude by providing an up-to-date bibliography on the subject.