English

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.

Keywords

Cite

@article{arxiv.2510.11435,
  title  = {The Dirac equation and the Quantum Potential},
  author = {Calum Robson},
  journal= {arXiv preprint arXiv:2510.11435},
  year   = {2025}
}

Comments

15 Pages

R2 v1 2026-07-01T06:34:05.090Z