The Heisenberg spinor field classification and its interplay with the Lounesto\u2019s classification

Marcos R. A. Arcodía,Roldão da Rocha,Mauricio Bellini

doi:10.1140/epjc/s10052-019-6778-4

Abstract

Dirac linear spinor fields were obtained from non-linear Heisenberg spinors, in the literature. Here we extend that idea by considering not only Dirac spinor fields but spinor fields in any of the Lounesto’s classes. When one starts considering all these classes of fields, the question of providing a classification for the Heisenberg spinor naturally arises. In this work the classification of Heisenberg spinor fields is derived and scrutinized, in its interplay with the Lounesto’s spinor field classification.

Highlights

On the other hand, very little is known about the Heisenberg spinors in this context
The Heisenberg equation governs the dynamics of diverse spinor fields, constituting the Inomata–McKinley spinor fields one of its particular solution
Some regular spinor fields can be constructed upon appropriate linear mixtures of Inomata–McKinley spinor fields [21]

Summary

Introduction

Very little is known about the Heisenberg spinors in this context. Some regular spinor fields can be constructed upon appropriate linear mixtures of Inomata–McKinley spinor fields [21]. Dirac spinor fields were described by a non-linear mixture of Heisenberg spinors fields [22], to show that neutrinos are quantum field states of Heisenberg spinor fields. A byproduct of our development in this paper is, in particular, to emulate previous constructions that describe Dirac spinor fields as Heisenberg ones, to further encompass all types of spinor fields in both the Heisenberg and the Lounesto’s classification. This paper is organized as follows: after reviewing the Lounesto’s classification and presenting the bilinear covariants, the regular and singular spinor fields, Sect. 3 devotes to derive and present the Heisenberg classification of spinor fields and to scrutinize the interplay between Heisenberg spinor fields and the ones in the Lounesto’s classification.

Lounesto’s classification and ramifications

Heisenberg spinor fields classification

Conclusions