November 30, 2021 to December 2, 2021
Le Bois-Marie
Europe/Paris timezone

Geometry, Matter and Physics (in person)

Dec 1, 2021, 12:00 PM
Centre de conférences Marilyn et James Simons (Le Bois-Marie)

Centre de conférences Marilyn et James Simons

Le Bois-Marie

35, route de Chartres 91440 Bures-sur-Yvette


Richard Kerner (LPTMC, Sorbonne-Université)


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.

Presentation materials