Internal quark symmetries and colour SU(3) entangled with Z_3-graded Lorentz algebra
arXiv:2012.05335 · doi:10.1016/j.nuclphysb.2021.115529
Abstract
In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the colour, the flavour, and broken providing the family triplets. \noindent In this paper we argue that internal and external (i.e. space-time) symmetries are entangled at least in the colour sector in order to introduce the spinorial quark fields in a way providing all the internal quark's degrees of freedom which do appear in the Standard Model. Because the colour algebra is endowed with natural -graded discrete automorphisms, in order to introduce entanglement the -graded version of Lorentz and Poincaré algebras with their realizations are considered. The colour multiplets of quarks are described by -component colour Dirac equations, with a -graded triplet of masses (one real and a Lee-Wick complex conjugate pair). We argue that all quarks in the Standard Model can be described by the -component master quark sextet of -component coloured Dirac fields.
39 pages, 3 figures. This version is conformal with the revised version published in the journal (Nucl. Phys. B)