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arXiv · 2012.05335

Internal quark symmetries and colour SU(3) entangled with Z_3-graded Lorentz algebra

Richard Kerner·Jerzy Lukierski
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Abstract

In the current version of QCD the quarks are described by ordinary Dirac fields, organized in the following internal symmetry multiplets: the $SU(3)$ colour, the $SU(2)$ flavour, and broken $SU(3)$ providing the family triplets. \noindent In this paper we argue that internal and external (i.e. space-time) symmetries are entangled at least in the colour sector in order to introduce the spinorial quark fields in a way providing all the internal quark's degrees of freedom which do appear in the Standard Model. Because the $SU(3)$ colour algebra is endowed with natural $Z_3$-graded discrete automorphisms, in order to introduce entanglement the $Z_3$-graded version of Lorentz and Poincar\'e algebras with their realizations are considered. The colour multiplets of quarks are described by $12$-component colour Dirac equations, with a $Z_3$-graded triplet of masses (one real and a Lee-Wick complex conjugate pair). We argue that all quarks in the Standard Model can be described by the $72$-component master quark sextet of $12$-component coloured Dirac fields.

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Richard Kerner, Jerzy Lukierski. 2020-12-09. Internal quark symmetries and colour SU(3) entangled with Z_3-graded Lorentz algebra. https://doi.org/10.1016/j.nuclphysb.2021.115529

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