Аннотация:
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 colour
$SU(3)$ 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 $Z_3$ may play a crucial role in quark field dynamics.
We consequently apply the $Z_3$ symmetry to field multiplets
describing colour quark fields. Generalized Dirac equation for
coloured $12$-component spinors is introduced and its properties are
discussed. Imposing $Z_3$-graded Lorentz and Poincaré covariance
leads to enlargement of quark fields multiplets and incorporates
additional $Z_2 \times Z_3$ symmetry which leads
to the appearance of three generations (families) of distinct quark
doublets.
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