On the symmetries of elementary fermions

Abstract

This paper deals with the symmetries of elementary fermions and their derivation from fundamental physical principles such as the Lorentz invariance and from the spinor-helicity formalism employed to three-vectors. The generators of the Lorentz group are discussed, and the physics of the associated chiral spins is used to establish the chiral symmetry SU(2). The helicity of spin is defined which, when being applied to the hadronic isospin, yields the symmetry group SU(4). The Kronecker product of these two basic symmetries defines a unified symmetry SU(2)⊗SU(4)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$SU(2) \\otimes SU(4)$$\\end{document} of the basic light fermions, namely the chiral doublets of the single lepton and triple quarks of the first family. Breaking this symmetry, according to mechanisms that are used in the electroweak interactions of the Standard Model (SM) of quantum field theory, yields quantum electrodynamics (QED) with symmetry group U(1), weak interactions with symmetry group SU(2), and what we like to name quantum hadrodynamics (QHD, akin to quantum chromodynamics QCD of the SM) with symmetry group SU(3). The gauge bosons associated with QED and QHD remain massless, but the weak bosons and the V bosons, related to the transformation of the quarks into a lepton and vice versa, become massive by the Higgs mechanism. Their masses are defined by the Higgs vacuum and the two coupling constants involved in the unified model. The V-boson mass is predicted to be 35.4 GeV. Furthermore, a possible explanation of hadron confinement is given in terms of the two hadronic charge operators. Moreover, the concept of hypercharge as used in the SM is not needed. Various versions of the extended Dirac equation that include the above symmetry groups are derived.