Operational dynamical modeling of spin 1/2 relativistic particles: The Dirac equation and its classical limit

Renan Cabrera, Andre G. Campos, Herschel A. Rabitz, Denys I. Bondar

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)2195-2207
Number of pages13
JournalEuropean Physical Journal: Special Topics
Volume227
Issue number15-16
DOIs
StatePublished - Mar 1 2019

All Science Journal Classification (ASJC) codes

  • Materials Science(all)
  • Physics and Astronomy(all)
  • Physical and Theoretical Chemistry

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