arXiv subjects

Calum Robson

Publications and source records attributed to Calum Robson.

2 recordsLinked to original sources

arXiv2025

The Dirac equation and the Quantum Potential

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.

quant-ph↗

arXiv2023

Self-Dual Maxwell Fields from Clifford Analysis

The study of complex functions is based around the study of holomorphic functions, satisfying the Cauchy-Riemann equations. The relatively recent field of Clifford Analysis lets us extend many results from Complex Analysis to higher dimensions. In this paper, I decompose the Cauchy-Riemann equations for a general Clifford algebra into grades using the Geometric Algebra formalism, and show that for the Spacetime Algebra $Cl(3,1)$ these equations are the equations for a self-dual source free Maxwell field, and for a massless uncharged Spinor. This shows a deep link between fundamental physics and the Clifford geometry of Spacetime.

math-ph↗