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A unified field theory from a complexified quaternion-octonion Dirac equation

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arxiv 2205.06657 v2 pith:JM4T7WB6 submitted 2022-04-27 physics.gen-ph hep-th

Juan Camilo Vélez Quiñones This is my paper · ORCID
classification physics.gen-phhep-th
keywords diracequationfieldunifiedalgebrafieldsmodelalgebraic
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It is set manifest an underlying algebraic structure of Dirac equation and solutions, in terms of Cl2 Clifford algebra projectors and ladder operators. From it, a scheme is proposed for constructing unified field theories by enlarging the pointed algebra. A toy unified matter field model is formulated, modifying Dirac equation with complex quaternions and octonions. The result describes a set of fermion fields with reminiscent properties of one standard model particle generation, exhibiting U(1) electromagnetism, SU(2) flavor and SU(3) color like symmetries, remarkably SU(2) induces frame fields, though further explorations are needed.

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  1. The Dirac equation in (split-)octonions: origins, variants, and modern context

    math-ph 2026-06 conditional novelty 5.0 of 10

    Four approaches to the Dirac equation in (split-)octonions are classified; a 2024 split-octonionic equation is shown identical to the 2006 2-factor form by structure-preserving rotation and relabeling.

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