Eur. Phys. J. Special Topics 227, 2195–2207 (2019)
https://doi.org/10.1140/epjst/e2018-800075-7

Regular Article

Operational dynamical modeling of spin 1/2 relativistic particles

The Dirac equation and its classical limit

¹ Princeton University Princeton, NJ 08544, USA
² Max Planck Institute for Nuclear Physics, 69117 Heidelberg, Germany
³ Tulane University, New Orleans, LA 70118, USA

^b e-mail: dbondar@tulane.edu

Received: 27 April 2018
Received in final form: 6 September 2018
Published online: 31 January 2019

Abstract

The formalism of Operational Dynamical Modeling [Bondar et al., Phys. Rev. Lett. 109, 190403 (2012)] is employed to analyze dynamics of spin half relativistic particles. We arrive at the Dirac equation from specially constructed relativistic Ehrenfest theorems by assuming that the coordinates and momenta do not commute. Forbidding creation of antiparticles and requiring the commutativity of the coordinates and momenta lead to classical Spohn’s equation [Spohn, Ann. Phys. 282, 420 (2000)]. Moreover, Spohn’s equation turns out to be the classical Koopman-von Neumann theory underlying the Dirac equation.