# Combinatorics and Arithmetic for Physics: special days

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

## Geometry, Matter and Physics (in person)

1 Dec 2021, 12:00
50m
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

### 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.

### Presentation Materials

 cap2021-Kerner.pdf Vidéo