Abstract
A generation of leptons and quarks and the gauge symmetries of the Standard Model can be obtained from the Clifford algebra ℂℓ6. An instance of ℂℓ6 is implicitly generated by the Dirac algebra combined with the electroweak symmetry, while the color symmetry gives another instance of ℂℓ6 with a Witt decomposition. The minimal mathematical model proposed here results by identifying the two instances of ℂℓ6. The left ideal decomposition generated by the Witt decomposition represents the leptons and quarks, and their antiparticles. The SU(3)c and U(1)em symmetries 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.
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