Z_3 - graded colour Dirac equations for quarks, confinement and generalized Lorentz symmetries
Abstract
We propose a modification of standard QCD description of the colour triplet of quarks describing quark fields endowed with colour degree of freedom by introducing a 12-component colour generalization of Dirac spinor, with built-in Z_3 grading playing an important algebraic role in quark confinement. In "colour Dirac equations" the SU(3) colour symmetry is entangled with the Z_3-graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by Z_3 maps. The generalized Lorentz covariance requires simultaneous presence of 24 colour Dirac multiplets, which lead to the description of all internal symmetries of quarks: besides SU(3) \times SU(2) \times U(1), the flavour symmetries and three quark families.
Cite
@article{arxiv.1901.10936,
title = {Z_3 - graded colour Dirac equations for quarks, confinement and generalized Lorentz symmetries},
author = {Richard Kerner and Jerzy Lukierski},
journal= {arXiv preprint arXiv:1901.10936},
year = {2019}
}
Comments
LaTeX, 14 pages, no figures; v2 improved LaTeX format and small corrections in Sect 3, v3 changes in Introduction: mainly formula (2) deleted and formula (3) shifted to Sect.2;v4 small change in formula (27) and exposed role of Lorentz-covariant doublets of colour multiplets v5 extended version by three pages, new content of Sect 4