Octonionic Dirac Equation
Stefano De Leo, Khaled Abdel-Khalek
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.
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