Dixon-Rosenfeld lines and the Standard Model

David Chester; Alessio Marrani; Daniele Corradetti; Raymond Aschheim; Klee Irwin

doi:10.1140/epjc/s10052-023-12006-8

2024 Impact factor 4.8

Particles and Fields

Open Access

Eur. Phys. J. C (2023) 83: 849
https://doi.org/10.1140/epjc/s10052-023-12006-8

Regular Article - Theoretical Physics

Dixon-Rosenfeld lines and the Standard Model

David Chester¹^a, Alessio Marrani²^b, Daniele Corradetti³^c, Raymond Aschheim¹^d and Klee Irwin¹^e

¹ Quantum Gravity Research, Topanga Canyon Rd 101 S, 90290, Topanga, CA, USA
² Instituto de Física Teorica, Departamento de Física, Universidad de Murcia, Campus de Espinardo, 30100, Murcia, Spain
³ Departamento de Matemática, Universidade do Algarve, Campus de Gambelas, 8005-139, Faro, Portugal

^a DavidC@QuantumGravityResearch.org
^b alessio.marrani@um.es
^c a55944@ualg.pt
^d Raymond@QuantumGravityResearch.org
^e Klee@QuantumGravityResearch.org

Received: 30 March 2023
Accepted: 5 September 2023
Published online: 22 September 2023

Abstract

We present three new coset manifolds named Dixon-Rosenfeld lines that are similar to Rosenfeld projective lines except over the Dixon algebra $C \otimes H \otimes O$ $\mathbb {C}\otimes \mathbb {H}\otimes \mathbb {O}$ . Three different Lie groups are found as isometry groups of these coset manifolds using Tits’ formula. We demonstrate how Standard Model interactions with the Dixon algebra in recent work from Furey and Hughes can be uplifted to tensor products of division algebras and Jordan algebras for a single generation of fermions. The Freudenthal–Tits construction clarifies how the three Dixon-Rosenfeld projective lines are contained within $C \otimes H \otimes J_{2} (O)$ $\mathbb {C}\otimes \mathbb {H}\otimes J_{2}(\mathbb {O})$ , $O \otimes J_{2} (C \otimes H)$ $\mathbb {O}\otimes J_{2}(\mathbb {C}\otimes \mathbb {H})$ , and $C \otimes O \otimes J_{2} (H)$ $\mathbb {C}\otimes \mathbb {O}\otimes J_{2}(\mathbb {H})$ .

© The Author(s) 2023

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