Octonionic Dirac Equation
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× 8 real matrices (a translation is also given for 4× 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.
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.