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Octonionic Dirac Equation

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arxiv hep-th/9609033 v1 pith:Y6WXRZEP submitted 1996-09-03 hep-th

Stefano De Leo , Khaled Abdel-Khalek (Lecce) This is my paper · ORCID
classification hep-th
keywords octonionicequationdiracmatricesoperatorstimestranslationwave
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abstract

In order to obtain a consistent formulation of octonionic quantum mechanics (OQM), we introduce left-right barred operators. Such operators enable us to find the translation rules between octonionic numbers and $8\times 8$ real matrices (a translation is also given for $4\times 4$ complex matrices). We develop an octonionic relativistic free wave equation, linear in the derivatives. Even if the wave functions are only one-component we show that four independent solutions, corresponding to those of the Dirac equation, exist.

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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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