Research PapersOpen Access

The underlying geometry of the CAM gauge model of the Standard Model of particle physics

Brian Jonathan Wolk

3551 Blair Stone Road, Suite 105, Tallahassee, FL 32301, USA

E-mail Address: Brian.Jonathan.Wolk@gmail.com

https://doi.org/10.1142/S0217751X20500372Cited by:7 (Source: Crossref)

Abstract

The Composition Algebra-based Methodology (CAM) [B. Wolk, Pap. Phys.9, 090002 (2017); Phys. Scr.94, 025301 (2019); Adv. Appl. Clifford Algebras27, 3225 (2017); J. Appl. Math. Phys.6, 1537 (2018); Phys. Scr.94, 105301 (2019), Adv. Appl. Clifford Algebras30, 4 (2020)], which provides a new model for generating the interactions of the Standard Model, is geometrically modeled for the electromagnetic and weak interactions on the parallelizable sphere operator fiber bundle $B_{n} = (T 𝕄, S^{n} \to 𝒮^{n}, S O (n + 1), π)$ consisting of base space, the tangent bundle $T 𝕄$ of space–time $𝕄$ , projection operator $π$ , the parallelizable spheres $S^{n} = {S^{1}, S^{3}}$ conceived as operator fibers $S^{n} \to 𝒮^{n}$ attaching to and operating on $T_{p} 𝕄$ $\forall p \in 𝕄$ as $p$ varies over $𝕄$ , and as structure group, the norm-preserving symmetry group $S O (n + 1)$ for each of the division algebras which is simultaneously the isometry group of the associated unit sphere. The massless electroweak $S U {(2)}_{L} \otimes U {(1)}_{Y}$ Lagrangian is shown to arise from $B_{3 \otimes 1}$ ’s generation of a local coupling operation on sections of Dirac spinor and Clifford algebra bundles over $𝕄$ . Importantly, CAM is shown to be a new genre of gauge theory which subsumes Yang–Mills Standard Model gauge theory. Local gauge symmetry is shown to be at its core a geometric phenomenon inherent to CAM gauge theory. Lastly, the higher-dimensional, topological architecture which generates CAM from within a unified eleven $(1, 10)$ -dimensional geometro-topological structure is introduced.

Keywords:

PACS: 12.10.Dm, 12.90.+b

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Vol. 35, No. 07

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Received 21 September 2019

Accepted 4 March 2020

Published: 7 April 2020

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This is an Open Access article published by World Scientific Publishing Company. It is distributed under the terms of the Creative Commons Attribution 4.0 (CC BY) License which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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The underlying geometry of the CAM gauge model of the Standard Model of particle physics

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