Octonionic Version of Dirac Equations

Details Octonionic Version of Dirac Equations Octonionic Version of Dirac Equations

2005-05-11

arxiv.org/abs/hep-th/0505101v2

Int.J.Mod.Phys.A21:3513-3524,2006

Physics

High Energy Physics

High Energy Physics - Theory

Version accepted by Int. J Mod. Phys

Scientific paper

10.1142/S0217751X06028436

It is shown that a simple continuity condition in the algebra of split octonions suffices to formulate a system of differential equations that are equivalent to the standard Dirac equations. In our approach the particle mass and electro-magnetic potentials are part of an octonionic gradient function together with the space-time derivatives. As distinct from previous attempts to translate the Dirac equations into different number systems here the wave functions are real split octonions and not bi-spinors. To formulate positively defined probability amplitudes four different split octonions (transforming into each other by discrete transformations) are necessary, rather then two complex wave functions which correspond to particles and antiparticles in usual Dirac theory.

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