Operational Dynamical Modeling of spin 1/2 relativistic particles: the Dirac equation and its classical limit
arXiv:1805.08243 · doi:10.1140/epjst/e2018-800075-7
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.
References in corpus (32)
- Two-Dimensional Gas of Massless Dirac Fermions in Graphene
- Topological Insulators
- Chiral tunneling and the Klein paradox in graphene
- Quantum simulation of the Dirac equation
- Observing Zitterbewegung in Ultracold Atoms
- Direct observation of chiral currents and magnetic reflection in atomic flux lattices
- Quantum Speed Limits Across the Quantum-to-Classical Transition
- Dirac Equation For Cold Atoms In Artificial Curved Spacetimes
- Operational Dynamic Modeling Transcending Quantum and Classical Mechanics
- Universal Local symmetries and non-superposition in classical mechanics
- Confining stationary light: Dirac dynamics and Klein tunneling
- Semiclassical limit of the Dirac equation and spin precession
- Wigner phase space distribution as a wave function
- Efficient method to generate time evolution of the Wigner function for open quantum systems
- Quantum Simulations of Relativistic Quantum Physics in Circuit QED
- Identifying the Stern-Gerlach force of classical electron dynamics
- Wigner-Lindblad equations for quantum friction
- Hilbert Space Structure in Classical Mechanics: (I)
- Dirac open quantum system dynamics: formulations and simulations
- Zitterbewegung and semiclassical observables for the Dirac equation
- Simulation of Zitterbewegung by modelling the Dirac equation in Metamaterials
- Hilbert Space Structure in Classical Mechanics: (II)
- No thermalization without correlations
- The Wigner function in the relativistic quantum mechanics
- Conceptual inconsistencies in finite-dimensional quantum and classical mechanics
- Non-classicality of positive relativistic Wigner function
- Efficient computations of quantum canonical Gibbs state in phase space
- Wigner representation of the rotational dynamics of rigid tops
- Ehrenfest principle and unitary dynamics of quantum-classical systems with general potential interaction
- Quantum mechanics of a free particle from properties of the Dirac delta function
- Classical Propagation in the Quantum Inverted Oscillator
- Quantum friction: environment engineering perspectives