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Journal Article

The standard model, the Pati-Salam model, and "Jordan geometry"


Farnsworth,  Shane
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Boyle, L., & Farnsworth, S. (2020). The standard model, the Pati-Salam model, and "Jordan geometry". New Journal of Physics. doi:10.1088/1367-2630/ab9709.

Cite as: https://hdl.handle.net/21.11116/0000-0005-1BF7-7
We argue that the ordinary commutative-and-associative algebra of spacetime
coordinates (familiar from general relativity) should perhaps be replaced, not
by a noncommutative algebra (as in noncommutative geometry), but rather by a
Jordan algebra (leading to a framework which we term "Jordan geometry"). We
present the Jordan algebra (and representation) that most nearly describes the
standard model of particle physics, and we explain that it actually describes a
certain (phenomenologically viable) extension of the standard model: by three
right-handed (sterile) neutrinos, a complex scalar field $\varphi$, and a
$U(1)_{B-L}$ gauge boson which is Higgsed by $\varphi$. We then note a natural
extension of this construction, which describes the $SU(4)\times
SU(2)_{L}\times SU(2)_{R}$ Pati-Salam model. Finally, we discuss a simple and
natural Jordan generalization of the exterior algebra of differential forms.