The Standard Model Algebra - a summary

Abstract

Abstract. A generation of leptons and quarks and the gauge symmetries of the Standard Model can be obtained from the Clifford algebra C 6. An instance of C 6 is implicitly generated by the Dirac algebra combined with the electroweak symmetry, while the color symmetry gives another instance of C 6 with a Witt decomposition. The minimal mathematical model proposed here results by identifying the two instances of C 6. 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 sin 2 θW = 0.25. The model shares common features with previously known models, particularly with Chisholm

Spin(11, 3), particles, and octonions

“…The split case Spin (7,7) was advocated in an earlier work of this author [18]. Other papers related to the present work are a series of papers by C. Stoica [19], [20], [21], and a recent paper [22].…”

“…Indeed, the conditions reducing to so(6) = su(4) are the 6 conditions w i4 = 0. Intersected with (21) this gives us su (3).…”

Thinking Non Locally: The Atemporal Roots of Particle Physics

“…To our best knowledge, the peculiarity of this role distinguishes our proposal from other algebraic models, available in literature, also aimed at the theoretical justification of the Standard Model. In particular we want to briefly discuss some correspondences and differences with the recent (and fascinating) works of Furey [19][20][21][22] and Stoica [23]. It is first necessary to consider that the questions explicitly formulated by both these authors as motivations for their research are the same ones that we have set ourselves and which we have illustrated in the introductory part of this work.…”

“…A strict test for every algebraic approach is represented by the calculation of the mixing angles, because the setting of such a calculation depends on the level (dynamic or timeless) to which the superposition principle appears. While, to our knowledge, nothing has been done for the mixing of quark flavors and neutrino oscillations, Stoica has derived a good estimate of the Weinberg angle [23]. His calculation is based on an algebraic structure directly implanted on QFT operators; the duplication of this result is therefore an open problem for our approach.…”