PIRSA:21020008

Video URL

https://pirsa.org/21020008

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

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

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

          @misc{ scivideos_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 for Theoretical Physics},
            year = {2021},
            month = {feb},
            note = {PIRSA:21020008 see, \url{https://scivideos.org/pirsa/21020008}}
          }

Michel Dubois-Violette University of Paris-Saclay

Talk numberPIRSA:21020008
DOI10.48660/21020008
Source RepositoryPIRSA
Collection
Talk Type Conference
Subject

Abstract

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.