Constraints on mapping the Lounesto's Classes

TL;DR

This paper introduces a new method to classify spinors within Lounesto's six classes by analyzing phase factors, eliminating the need to evaluate bilinear forms, and explores class transmutation possibilities.

Contribution

A novel algorithm for classifying spinors in Lounesto's framework based on phase analysis, applicable to both regular and singular spinors, simplifying the classification process.

Findings

The method accurately classifies spinors without bilinear form calculations.

It enables analysis of potential transmutation between classes.

Applicable to both regular and singular spinors.

Abstract

The so-called Lounesto's classification engenders six distinct classes of spinors, divided into two sectors: one composed by regular spinors (single-helicity spinors) and the other composed by singular spinors (comprising dual-helicity spinors). In the present essay we develop a mechanism to fully define the right class within the Lounesto's classification a spinor belongs to, without necessity to evaluate the 16 bilinear forms. The analysis lies in the following criteria: a judicious inspection of the phases factor present in both spinor's components. Thus, the machinery developed here works for both regular and singular spinors. Taking advantage of the present algorithm, we analyse, under certain conditions, the possibility to transmute between the six classes.