The Dirac equation and the Quantum Potential
Quantum Physics
2025-10-14 v1 Mathematical Physics
math.MP
Abstract
One key theme of Basil Hiley's work was the development of David Bohm's approach to Quantum Mechanics; in particular the concept of the quantum potential. Another theme was the importance of Clifford Algebras in fundamental physics. In this paper I will combine these approaches by looking at how the quantum potential can be extended to the Dirac equation. I will begin by discussing the geometry of the Dirac equation, and how this is made clearer by the use of Clifford algebras .Next, I will rewrite the Cl(2) Dirac wavefunction in Polar form, and show that new behaviour arises due to topological nonlocality. Finally, I discuss the relationship between the Dirac and Schroedinger equations.
Cite
@article{arxiv.2510.11435,
title = {The Dirac equation and the Quantum Potential},
author = {Calum Robson},
journal= {arXiv preprint arXiv:2510.11435},
year = {2025}
}
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15 Pages