# Combinatorics and Arithmetic for Physics: special days

Dec 2 – 3, 2020
Le Bois-Marie
Europe/Paris timezone

## Unifying Colour $SU(3)$ with ${\mathbb Z}_3$-Graded Lorentz-Poincaré Algebra

Dec 3, 2020, 5:20 PM
50m

### Speaker

Richard Kerner (LPTMC, Sorbonne Université, Paris)

### Description

A generalization of Dirac’s equation is presented, incorporating the three-valued colour variable in a way which makes it intertwine with the Lorentz transformations. We show how the Lorentz-Poincaré group must be extended to accomodate both $SU(3)$ and the Lorentz transformations. Both symmetries become intertwined, so that the system can be diagonalized only after the sixth iteration, leading to a six-order characteristic equation with complex masses similar to those of the Lee-Wick model. The spinorial representation of the ${\mathbb Z}_3$-graded Lorentz algebra is presented, and its vectorial counterpart acting on a ${\mathbb Z}_3$-graded extension of the Minkowski space-time is also constucted. Application to new formulation of the QCD and its gauge-field content is briefly evoked.

### Presentation materials

 CAP20_Kerner.pdf Vidéo