Contemplations on Dirac's equation in quaternionic coordinates

TL;DR

This paper explores a quaternionic coordinate formulation of Dirac's equation, which simplifies its structure by removing Dirac matrices but introduces unique peculiarities that require interpretation.

Contribution

It presents a novel quaternionic coordinate approach to Dirac's equation, enhancing formal elegance and offering new perspectives on its mathematical structure.

Findings

Eliminates the need for Dirac matrices in the equation

Identifies peculiarities arising from quaternionic formulation

Provides interpretations for these peculiarities

Abstract

A formulation of Dirac's equation using complex-quaternionic coordinates appears to yield an enormous gain in formal elegance, as there is no longer any need to invoke Dirac matrices. This formulation, however, entails several peculiarities, which we investigate and attempt to interpret.