ELKO in Polar Form

TL;DR

This paper explores the polar form of ELKO spinors, revealing new structural insights through a novel adjunction procedure that preserves covariance under spin transformations.

Contribution

It introduces a polar decomposition of ELKO spinors and a new adjunction method, providing deeper understanding of their structure and transformation properties.

Findings

ELKO can be expressed in a polar form with a real module and complex phase

A new adjunction procedure for ELKO preserves covariance under spin transformations

Structural properties of ELKO are clarified in their polar decomposition

Abstract

In this paper, we consider the theory of ELKO written in their polar form, in which the spinorial components are converted into products of a real module times a complex unitary phase while the covariance under spin transformations is still maintained: we derive an intriguing conclusion about the structure of ELKO in their polar decomposition when seen from the perspective of a new type of adjunction procedure defined for ELKO themselves. General comments will be given in the end.