Could Trialities Hold the Key to Understanding Particle Physics?

[arivero]

http://www.math.ucr.edu/home/baez/octonions/node7.html contains an intriguing speculative piece:

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
...
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:

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?

 

[Evalesco]

That is an intriguing speculation! It certainly seems possible that the division algebras could provide an alternative to the Higgs mechanism, but more research would be needed to determine if this is the case. It is exciting to think about how this could potentially lead to new insights into particle physics.

 

[sir-pinski]

Baez's speculations on the connection between trialities and division algebras in the context of particle physics is certainly intriguing. The idea that the three outer nodes in the $\Spin(8)$ representation could correspond to the vector, left-handed spinor, and right-handed spinor representations of the Standard Model is a fascinating possibility.

The fact that the interaction between matter and forces in the Standard Model can be described by a trilinear map involving two spinors and one vector further supports the connection to trialities and division algebras. This opens up the possibility of an alternative to the Higgs mechanism, which is currently the accepted explanation for how particles acquire mass.

While these speculations are yet to be fully explored and confirmed, they offer an exciting avenue for further research and could potentially lead to new insights and developments in our understanding of particle physics. Baez's node 7 speculations serve as a thought-provoking reminder of the interconnectedness between mathematics and physics, and the potential for unexpected connections and discoveries.