Extended Z3-graded Lorentz symmetry and quark chromodynamics

Abstract

We propose a modification of standard QCD description of the color triplet of quarks by introducing a 12-component color generalization of Dirac spinor, with built-in [Formula: see text] grading playing an important algebraic role in quark confinement. In the “color Dirac equations” the [Formula: see text] color symmetry is entangled with the [Formula: see text]-graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by [Formula: see text]-graded maps. The generalized Lorentz covariance requires simultaneous presence of 12 color Dirac multiplets, which lead to the description of all internal symmetries of quarks: besides [Formula: see text], the flavor symmetries and three quark families. We also discuss the generalized gauge fields and show how the Standard Model content appears naturally due to the overall [Formula: see text] symmetry.