TL;DR
This paper introduces a new relativistic wave equation based on complexified quaternions, which, despite having one-component wave functions, reproduces the four solutions characteristic of the Dirac equation, bridging complex and quaternionic quantum mechanics.
Contribution
It develops a one-component relativistic wave equation on complexified quaternions that yields Dirac-like solutions, offering a novel quaternionic approach to quantum mechanics.
Findings
Four independent solutions analogous to Dirac solutions
Establishment of translations between complex and quaternionic quantum mechanics
Demonstration of a relativistic wave equation with one-component wave functions
Abstract
We develop a relativistic free wave equation on the complexified quaternions, 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. A partial set of translations between complex and complexified quaternionic quantum mechanics may be defined.
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