Operational Dynamical Modeling of spin 1/2 relativistic particles: the Dirac equation and its classical limit
Quantum Physics
2019-02-14 v1
Abstract
The formalism of Operational Dynamical Modeling [Phys. Rev. Lett. {\bf 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 [Ann. Phys. {\bf 282}, 420 (2000)]. Moreover, Spohn's equation turns out to be the classical Koopman-von Neumann theory underlying the Dirac equation.
Keywords
Cite
@article{arxiv.1805.08243,
title = {Operational Dynamical Modeling of spin 1/2 relativistic particles: the Dirac equation and its classical limit},
author = {Renan Cabrera and Andre Campos and Herschel A. Rabitz and Denys I. Bondar},
journal= {arXiv preprint arXiv:1805.08243},
year = {2019}
}