Loading [MathJax]/jax/output/HTML-CSS/jax.js
Volume 376 - Corfu Summer Institute 2019 "School and Workshops on Elementary Particle Physics and Gravity" (CORFU2019) - Humboldt Kolleg Frontiers in Physics: From the Electroweak to the Planck Scales
Jordan algebra approach to finite quantum geometry
I. Todorov
Full text: pdf
Published on: August 18, 2020
Abstract
The exceptional euclidean Jordan algebra J83, consisting of 3×3 hermitian octonionic matrices, appears to be tailor made for the internal space of the three generations of quarks and leptons. The maximal rank subgroup of the authomorphism group F4 of J83 that respects the lepton-quark splitting is (SU(3)c×SU(3)ew)/Z3. Its restriction to the special Jordan subalgebra J82J83, associated with a single generation of fundamental fermions, is precisely the symmetry group S(U(3)×U(2)) of the Standard Model. The Euclidean extension H16(C)H16(C) of J82, the subalgebra of hermitian matrices of the complexification of the associative envelope of J82, involves 32 primitive idempotents giving the states of the first generation fermions. The triality relating left and right Spin(8) spinors to 8-vectors corresponds to the Yukawa coupling of the Higgs boson to quarks and leptons.
DOI: https://doi.org/10.22323/1.376.0163
How to cite

Metadata are provided both in article format (very similar to INSPIRE) as this helps creating very compact bibliographies which can be beneficial to authors and readers, and in proceeding format which is more detailed and complete.

Open Access
Creative Commons LicenseCopyright owned by the author(s) under the term of the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.