Spinors beyond Dirac, Weyl and Majorana: the Flag-Dipoles

TL;DR

This paper explores the classification of 1/2-spin spinor fields, focusing on the less-studied flag-dipole class, and discusses their properties and representatives within the Lounesto framework.

Contribution

It provides a detailed analysis of flag-dipole spinor fields, expanding the understanding of singular spinors beyond Dirac, Weyl, and Majorana types.

Findings

Classification of spinor fields into six classes based on bilinear covariants

Identification and characterization of flag-dipole spinor fields

Discussion of the properties and representatives of each class

Abstract

We recall the Lounesto classification of 1/2-spin spinor fields, based on the vanishing of spinorial bilinear quantities: the classes are the regular spinor fields (i.e. the Dirac field), as well as singular spinor fields, also known as flag-dipole spinor fields, admitting two limiting sub-classes, given by the dipole spinors (i.e. the Weyl spinor) and the flagpole spinors (i.e. the Majorana spinor). We discuss each class in terms of its representatives, with particular emphasis upon the flag-dipole spinor fields.