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

doi:10.1140/epjst/e2018-800075-7

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 journal › Article › peer-review

4 Scopus citations

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 language	English (US)
Pages (from-to)	2195-2207
Number of pages	13
Journal	European Physical Journal: Special Topics
Volume	227
Issue number	15-16
DOIs	https://doi.org/10.1140/epjst/e2018-800075-7
State	Published - Mar 1 2019

All Science Journal Classification (ASJC) codes

General Materials Science
General Physics and Astronomy
Physical and Theoretical Chemistry

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10.1140/epjst/e2018-800075-7

Cite this

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

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{\textquoteright}s equation [Spohn, Ann. Phys. 282, 420 (2000)]. Moreover, Spohn{\textquoteright}s equation turns out to be the classical Koopman-von Neumann theory underlying the Dirac equation.",

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AU - Campos, Andre G.

AU - Rabitz, Herschel A.

AU - Bondar, Denys I.

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N2 - 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.

AB - 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.

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

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