The Dirac Operator and the Bohm-Hiley Approach

Abstract Two key themes of Basil Hiley’s work were the development of David Bohm’s approach to Quantum Mechanics and the importance of Clifford Algebras in fundamental physics. In this paper I will combine these themes by beginning to examine the mathematics of Dirac operators within the Bohm-Hiley approach. I will begin by discussing the geometric interpretation of Dirac operators, 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.