Fermion Colour and Flavour Originating from Multiple Representations of the Lorentz Group and Clifford Algebra

Abstract

Where do such fermion properties as colour and flavour come from? We attempt to give a possible answer to this question in our paper. For that purpose we use the reducible (1/2,1/2) representation of the Lorentz group. Then the fermion corresponds to a doublet, each component of which can be described by the standard Dirac equation. In this way we conclude that quark and lepton, when being considered as doublets, originate from the discussed multiple representations of the Lorentz group (LG) and the related Clifford algebra. In particular the threefold colour degree of freedom emerges naturally, and similarly the threefold generation degree, both being enabled essentially by the fact that the SU(2) group has three generators given by the Pauli matrices. The Dirac spinor, or for zero mass the chiral Weyl spinor, remains the building block of that theory.