Relativity and Cosmology

Octonionic Non-Associativity and the Emergence of Particle Physics

Authors: Rüdiger Giesel

Weformulate a particle-physics sector in an octonionic projection framework in which the Standard Model is interpreted as the low-energy associative projection of a deeper non-associative field dynamics. The fundamental objects arethree octonion-valued fields ΨI ∈ O, I = 1,2,3, whose non-associative content is measured by the octonionic associator [Ψ1,Ψ2,Ψ3] = (Ψ1Ψ2)Ψ3− Ψ1(Ψ2Ψ3). A positive semidefinite associator potential dynamically suppresses nonassociative excitations at low energies and selects local associative subalgebras. We show how the chain O → Hphys → C motivates the emergence of complex quantum fields and Standard-Model-like residual gauge sectors related to SU(3)c, SU(2)L, and U(1)Y. We emphasize that the exact chiral hypercharge spectrum is not derived here; it requires an explicit projector representation.In this construction the associator is not merely an algebraic obstruction, but a dynamical source for projection, symmetry breaking, generation structure, mass hierarchy corrections, neutrino mixing corrections, Higgs-sector deformations, and possible fifth-force phenomenology. We briefly distinguish this proposal from division-algebraic Standard-Model reconstructions, where octonions primarily encode particle representations and charge assignments; here the new ingredient is the promotion of the associator to a field-theoreticquantity. The framework provides a constrained octonionic projection mechanism leading to Standard-Model-like particle sectors, while the complete derivation of the observed chiral charge spectrum remains an open task.

Comments: 21 Pages.

Download: PDF

Submission history

[v1] 2026-06-07 00:27:21

Unique-IP document downloads: 0 times

ai.Vixra.org is a AI assisted e-print repository rather than a journal. Articles hosted may not yet have been verified by peer-review and should be treated as preliminary. In particular, anything that appears to include financial or legal advice or proposed medical treatments should be treated with due caution. ai.Vixra.org will not be responsible for any consequences of actions that result from any form of use of any documents on this website.

Add your own feedback and questions here:
You are equally welcome to be positive or negative about any paper but please be polite. If you are being critical you must mention at least one specific error, otherwise your comment will be deleted as unhelpful.