Extended Z3-graded Lorentz symmetry and quark chromodynamics

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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 [ ] grading playing an important algebraic role in quark confinement. In the “color Dirac equations” the [ ] color symmetry is entangled with the [ ]-graded generalization of Lorentz symmetry, containing three 6-parameter sectors related by [ ]-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 [ ], 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 [ ] symmetry.

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