The Standard Model Algebra - a summary

[摘要] A generation of leptons and quarks and the gauge symmetries of the Standard Model can be obtained from the Clifford algebra 6. An instance of 6is implicitly generated by the Dirac algebra combined with the electroweak symmetry, while the color symmetry gives another instance of 6with a Witt decomposition. The minimal mathematical model proposed here results by identifying the two instances of 6. The left ideal decomposition generated by the Witt decomposition represents the leptons and quarks, and their antiparticles. The SU(3)cand U(1)emsymmetries of the SM are the symmetries of this ideal decomposition. The patterns of electric charges, colors, chirality, weak isospins, and hypercharges, follow from this, without predicting additional particles or forces, or proton decay. The electroweak symmetry is present in its broken form, due to the geometry. The predicted Weinberg angle is given by sin2W= 0.25. The model shares common features with previously known models, particularly with Chisholm and Farwell, 1996, Trayling and Baylis, 2004, and Furey, 2016.

[发布机构] Department of Theoretical Physics, National Institute of Physics and Nuclear Engineering - Horia Hulubei, Bucharest, Romania^1

[效力级别] 力学 [学科分类] 力学，机械学

[关键词] Clifford algebra;Common features;Electroweak symmetry;Gauge symmetries;Ideal decompositions;Proton decay;The standard model