Unveiling a spinor field classification with non-Abelian gauge symmetries

TL;DR

This paper introduces a new classification scheme for spinor fields that incorporates non-Abelian gauge symmetries, extending Lounesto's classification to include multiplets and richer structures, with specific focus on SU(2) symmetry.

Contribution

It generalizes Lounesto's spinor classification to non-Abelian gauge symmetries, revealing new classes and structures, especially for SU(2) gauge fields.

Findings

Classification includes 14 mixed classes of spinor doublets.

Richer flagpole, dipole, and flag-dipole structures are identified.

Lounesto's classification is a special case within this broader framework.

Abstract

A spinor fields classification with non-Abelian gauge symmetries is introduced, generalizing the the U(1) gauge symmetries-based Lounesto's classification. Here, a more general classification, contrary to the Lounesto's one, encompasses spinor multiplets, corresponding to non-Abelian gauge fields. The particular case of SU(2) gauge symmetry, encompassing electroweak and electromagnetic conserved charges, is then implemented by a non-Abelian spinor classification, now involving 14 mixed classes of spinor doublets. A richer flagpole, dipole, and flag-dipole structure naturally descends from this general classification. The Lounesto's classification of spinors is shown to arise as a Pauli's singlet, into this more general classification.