Z3-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 by introducing a 12-component colour generalization of Dirac spinor, with built-in Z3 grading playing an important algebraic role in quark confinement. In “colour Dirac equations” the SU(3) colour symmetry is entangled with the Z3-graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by Z3 maps. The generalized Lorentz covariance requires simultaneous presence of 12 colour Dirac multiplets, which lead to the description of all internal symmetries of quarks: besides SU(3)×SU(2)×U(1), the flavour symmetries and three quark families. Keywords: Colour Dirac equation, Quarks confinement, Z3 grading, Generalized Lorentz symmetries