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Quaternionic Lorentz group and Dirac equation

Stefano De Leo
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Abstract

We formulate Lorentz group representations in which ordinary complex numbers are replaced by linear functions of real quaternions and introduce dotted and undotted quaternionic one-dimensional spinors. To extend to parity the space-time transformations, we combine these one-dimensional spinors into bi-dimensional column vectors. From the transformation properties of the two-component spinors, we derive a quaternionic chiral representation for the space-time algebra. Finally, we obtain a quaternionic bi-dimensional version of the Dirac equation.

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Stefano De Leo. 2001-03-16. Quaternionic Lorentz group and Dirac equation. https://arxiv.org/abs/hep-th/0103129

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