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

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.

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Item Permalink: http://hdl.handle.net/21.11116/0000-0005-1BF7-7 Version Permalink: http://hdl.handle.net/21.11116/0000-0006-A364-1
Genre: Journal Article

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 Creators:
Boyle, Latham, Author
Farnsworth, Shane1, Author              
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1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014              

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Free keywords: High Energy Physics - Theory, hep-th,High Energy Physics - Phenomenology, hep-ph,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP
 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.

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 Dates: 2019-10-252019-10-302020
 Publication Status: Published online
 Pages: v1: 16 pages; v2: references added
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 Table of Contents: -
 Rev. Method: -
 Identifiers: arXiv: 1910.11888
URI: http://arxiv.org/abs/1910.11888
DOI: 10.1088/1367-2630/ab9709
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Title: New Journal of Physics
  Abbreviation : New J. Phys.
Source Genre: Journal
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Publ. Info: Bristol : IOP Publishing
Pages: - Volume / Issue: - Sequence Number: - Start / End Page: - Identifier: ISSN: 1367-2630
CoNE: https://pure.mpg.de/cone/journals/resource/954926913666