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

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1910.11888.pdf

(Preprint), 228KB

Boyle+et+al_2020_New_J._Phys._10.1088_1367-2630_ab9709.pdf

(Publisher version), 265KB

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##### Citation

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

##### Abstract

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.

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.