TY - JOUR
T1 - Operational dynamical modeling of spin 1/2 relativistic particles
T2 - The Dirac equation and its classical limit
AU - Cabrera, Renan
AU - Campos, Andre G.
AU - Rabitz, Herschel A.
AU - Bondar, Denys I.
N1 - Publisher Copyright:
© 2019, EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/3/1
Y1 - 2019/3/1
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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U2 - 10.1140/epjst/e2018-800075-7
DO - 10.1140/epjst/e2018-800075-7
M3 - Article
AN - SCOPUS:85063404530
SN - 1951-6355
VL - 227
SP - 2195
EP - 2207
JO - European Physical Journal: Special Topics
JF - European Physical Journal: Special Topics
IS - 15-16
ER -