Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1999-05-17
Int.J.Theor.Phys. 37 (1998) 1945
Physics
High Energy Physics
High Energy Physics - Theory
29 pages, RevTex
Scientific paper
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). The use of a complex geometry allows us to overcome the hermiticity problem and define an appropriate momentum operator within OQM. As an application of our results, 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.
Abdel-Khalek Khaled
Leo Stefano de
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