# Finite quantum geometry, octonions and the theory of fundamental particles.

### APA

Dubois-Violette, M. (2021). Finite quantum geometry, octonions and the theory of fundamental particles.. Perimeter Institute. https://pirsa.org/21020008

### MLA

Dubois-Violette, Michel. Finite quantum geometry, octonions and the theory of fundamental particles.. Perimeter Institute, Feb. 08, 2021, https://pirsa.org/21020008

### BibTex

@misc{ pirsa_PIRSA:21020008, doi = {10.48660/21020008}, url = {https://pirsa.org/21020008}, author = {Dubois-Violette, Michel}, keywords = {Mathematical physics, Particle Physics, Quantum Fields and Strings}, language = {en}, title = {Finite quantum geometry, octonions and the theory of fundamental particles.}, publisher = {Perimeter Institute}, year = {2021}, month = {feb}, note = {PIRSA:21020008 see, \url{https://pirsa.org}} }

**Collection**

We will describe an approach to the theory of fundamental particlesbased on finite-dimensional quantum algebras of observables. We will explain why the unimodularity of the color group suggests an interpretation of the quarklepton symmetry which involves the octonions and leads to the quantum spaces underlying the Jordan algebras of octonionic hermitian 2 × 2 and 3 × 3 matrices as internal geometry for fundamental particles. In the course of this talk, we will remind shortly why the finite-dimensional algebras of observables are the finite-dimensional euclidean Jordan agebras and we will describe their classifications. We will also explain our differential calculus on Jordan algebras and the theory of connections on Jordan modules. It is pointed out that the above theory of connections implies potentially a lot of scalar particles.