http://www.math.ucr.edu/home/baez/octonions/node7.html contains an intriguing speculative piece:(adsbygoogle = window.adsbygoogle || []).push({});

Now, if we had an interaction vertex connecting a vector, a left-handed spinor and a right-handed spinor... What would we have? perhaps an alternative to the Higgs mechanism? Here the three outer nodes correspond to the vector, left-handed spinor and right-handed spinor representations of $\Spin (8)$, while the central node corresponds to the adjoint representation

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The construction of division algebras from trialities has tantalizing links to physics. In the Standard Model of particle physics, all particles other than the Higgs boson transform either as vectors or spinors. The vector particles are also called `gauge bosons', and they serve to carry the forces in the Standard Model. The spinor particles are also called `fermions', and they correspond to the basic forms of matter: quarks and leptons. The interaction between matter and the forces is described by a trilinear map involving two spinors and one vector. This map is often drawn as a Feynman diagram:

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# Baez's node 7 speculations

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