Speaker
Richard Kerner
(LPTMC, Sorbonne-Université)
Description
We show how the fundamental statistical properties of quantum fields combined with the superposition principle lead to continuous symmetries including the $SL(2, C)$ group and the internal symmetry groups $SU(2)$ and $SU(3)$. The exact colour symmetry is related to ternary $Z_{3}$-graded generalization of the fermionic commutation relations for quarks. A $Z_{3}$-graded generalization of the Dirac equation is presented, and its invariance properties are analyzed. They lead to an enlarged $Z_{3}$-graded Lorentz group, operating in the Hilbert space of quark states including flavors and generations.
