On isospin and flavour of leptons and quarks

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.