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arXiv · 2111.11393

Quaternionic Dirac free particle

Sergio Giardino
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Abstract

We solve the quaternionic Dirac equation ($\mathbbm H$DE) in the real Hilbert space, and we ascertain that their free particle solutions set comprises eight elements in the case of a massive particle, and a four elements solution set in the case of a massless particle, a richer situation when compared to the four elements solutions set of the usual complex Dirac equation ($\mathbbm C$DE). These free particle solutions were unknown in the previous solutions of anti-hermitian quaternionic quantum mechanics, and constitute an essential element in order to build a quaternionic quantum field theory ($\mathbbm H$QFT).

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Sergio Giardino. 2021-11-22. Quaternionic Dirac free particle. https://doi.org/10.1142/s0217751x21502572

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