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.
Highlights
It is well known that colour symmetries play a double role - they describeSU(3) gauge symmetry group in QCD and are linked with quark confinement, which is obtained usually as dynamical consequence of strong forces between quarks growing linearly with their spatial separation.In the present paper we would like to propose an alternative algebraic approach to the confining aspect of colour symmetries
For that purpose we replace the usual tensor product of Lorentz and colour SU(3) group actions by the entanglement of space-time and colour symmetries generated by the Z3 symmetry which plays an important role in the appearance of fractional electric and baryonic charges of quarks
We shall show that such an entanglement appears naturally when we generalize the derivation of the 4-component Dirac equation as given by particular Z2 × Z2 symmetric coupling of a pair of 2-component Pauli spinors ([3]), to the Z3 × Z2 × Z2 symmetry which unifies in a specific manner (see (13)) the system of six linear equations for six Pauli spinors
Summary
It is well known that colour symmetries play a double role - they describeSU(3) gauge symmetry group in QCD and are linked with quark confinement, which is obtained usually as dynamical consequence of strong forces between quarks growing linearly with their spatial separation (see e.g. [1], [2]).In the present paper we would like to propose an alternative algebraic approach to the confining aspect of colour symmetries. One can further argue that the lowest-dimensional spinor space on which act the generalized Lorentz transformations in a closed and faithful way describes six different types of coloured quarks.
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