2019/10/31 by Richard Kerner, Jerzy Lukierski
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1088/1742-6596/1416/1/012016
20 pages, 1 figure; submitted to Proceedings of ISOS26 Conference held in Prague, Czech Republik (08-012.07.2019); to appear in Journal of Physics (Conference Series). arXiv admin note: text overlap with arXiv:1801.01403; v2 corrected formula (31), version to appear in Journal of Physics, Conference Series
arxiv created 2019/11/14 · arxiv updated 2020/01/08
Colour SU(3) group is an exact symmetry of Quantum Chromodynamics, which describes strong interactions between quarks and gluons. Supplemented by two internal symmetries, SU(2) and U(1), it serves as the internal symmetry of the Standard Model, describing as well the electroweak interactions of quarks and leptons. The colourSU(3) symmetry is exact, while two other symmetries are broken by means of the Higgs-Kibble mechanism. The three colours and fractional quarks charges with values 1/3 and 2/3 suggest that the cyclic group Z3 may play a crucial role in quark field dynamics. In this paper we consequently apply the Z3 symmetry to field multiplets describing colour quark fields. Generalized Dirac equation for coloured 12-component spinors is introduced and its properties are discussed. Imposing Z3-graded Lorentz and Poincaré covariance leads to enlargement of quark fields multiplets and incorporates additional Z2 × Z3 symmetry which leads to the appearance of three generations (families) of distinct quark doublets.