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Toward an Octonionic World

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Abstract

In order to obtain a consistent formulation ofoctonionic quantum mechanics (OQM), we introduceleft/right-barred operators. Such operators enable us tofind the translation rules between octonionic numbers and 8 × 8 real matrices (a translation isalso given for 4 × 4 complex matrices). The use ofa complex geometry allows us to overcome the hermiticityproblem and define an appropriate momentum operator within OQM. As an application of our results,we develop an octonionic relativistic free waveequation, linear in the derivatives. Even if the wavefunctions are only one-component, we show that fourindependent solutions, corresponding to those of the Diracequation, exist.

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Authors
  1. Stefano De Leo
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  2. Khaled Abdel-Khalek
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Leo, S.D., Abdel-Khalek, K. Toward an Octonionic World. International Journal of Theoretical Physics 37, 1945–1985 (1998). https://doi.org/10.1023/A:1026617314160

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