On isospin and flavour of leptons and quarks
Extraterrestrial Physics Group, Institute for Experimental and Applied Physics, Christian Albrechts University at Kiel, Leibnizstraße 11, 24118, Kiel, Germany
2 Space Research Institute, Austrian Academy of Sciences, Schmiedlstraße 6, 8042, Graz, Austria
Accepted: 1 December 2022
Published online: 17 December 2022
Isospin emerges naturally from the Lorentz transformation of spinors, if they are based on the vector representation of the Lorentz group. The resulting extended Dirac equation for a massive spin-one-half fermion has two new additional degrees of freedom associated with the up and down components of isospin. This doublet is interpreted as describing the electron and neutrino. It is adjoined with the SU(2) symmetry group. The extended Dirac equation appears in six versions which are connected by similarity transformations. It is argued that this trait may explain the occurrence of the three families of the leptons and suggested that flavour arises genuinely from the algebraic properties of the extended Dirac equation. Its solutions are discussed and the physical role of isospin is elucidated. Isospin symmetry can be gauged, which leads to a weak-interaction-type theory and is valid for finite initial mass. Breaking the isospin SU(2) symmetry yields the correct electric charges of the particles by means of the electroweak unification procedures of the standard model.
© The Author(s) 2022. corrected publication 2023
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.