Correspondence between classical and Dirac-Pauli spinors in view of the Foldy-Wouthuysen transformation

Chen, Tsung-Wei; Chiou, Dah-Wei

doi:10.1103/physreva.89.032111

Cited by 11 publications

(24 citation statements)

References 34 publications

(53 reference statements)

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“…Bearing in mind that the spin was introduced as an intrinsic quantum feature of the electron [59,60], it may appear more appropriate to start from the Dirac equation to find classical models of charged particles with spin [61]. Such a classical model with a spin-dependent force can be derived from relativistic quantum theory by applying the correspondence principle to the von Neumann equation in the Foldy-Wouthuysen representation of the Dirac equation [62][63][64][65]. We call this the classical Foldy-Wouthuysen model below.…”

Section: Introductionmentioning

confidence: 99%

Spin-one-half particles in strong electromagnetic fields: Spin effects and radiation reaction

2017

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Various classical models of electrons including their spin degrees of freedom are commonly applied to describe the electron dynamics in strong electromagnetic fields. We demonstrate that different models can lead to different or even contradicting predictions regarding how the spin degree of freedom modifies the electron's orbital motion when the electron moves in strong electromagnetic fields. This discrepancy is rooted in the model-specific energy dependency of the spin-induced Stern-Gerlach force acting on the electron. The Frenkel model and the classical Foldy-Wouthuysen model are compared exemplarily in the nonrelativistic and the relativistic limits in order to identify parameter regimes where these classical models make different predictions. This allows for experimental tests of these models. In ultra strong laser setups in parameter regimes where effects of the Stern-Gerlach force become relevant, radiation-reaction effects are also expected to set in. We incorporate the radiation reaction classically via the Landau-Lifshitz equation and demonstrate that although radiation-reaction effects can have a significant effect on the electron trajectory, the Frenkel model and the classical Foldy-Wouthuysen model remain distinguishable also if radiation-reaction effects are taken into account. Our calculations are also suitable to verify the Landau-Lifshitz equation for the radiation reaction of electrons and other spin-1/2 particles.

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Section: Introductionmentioning

confidence: 99%

Spin-one-half particles in strong electromagnetic fields: Spin effects and radiation reaction

2017

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“…There are subtleties in connecting operators in the Foldy-Wouthuysen representation to physical observables [11,15,16]. For example, the velocity operator of the particle is given by the time derivative of the position operator in the Heisenberg picture.…”

Section: B Observables and Their Corresponding Operatorsmentioning

confidence: 99%

“…Furthermore, the classical limit of this is precisely the classical equation of motion for the rest frame spin [26]. It is thus clear that the operator σ in the Foldy-Wouthuysen representation gives the polarization of the electron in the electron rest frame [11,22,27]. Based on this it is possible to understand the form of the Hamiltonian (2).…”

Section: B Observables and Their Corresponding Operatorsmentioning

confidence: 99%

Relativistic kinetic equation for spin-1/2 particles in the long-scale-length approximation

2017

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In this paper we derive a fully relativistic kinetic theory for spin-1/2 particles and its coupling to Maxwell's equations, valid in the long scale-length limit, where the fields vary on a scale much longer than the localization of the particles; we work to first order in . Our starting point is a Foldy-Wouthuysen (FW) transformation, applicable to this regime, of the Dirac Hamiltonian. We derive the corresponding evolution equation for the Wigner quasi-distribution in an external electromagnetic field. Using a Lagrangian method we find expressions for the charge and current densities, expressed as free and bound parts. It is furthermore found that the velocity is non-trivially related to the momentum variable, with the difference depending on the spin and the external electromagnetic fields. This fact that has previously been discussed as "hidden momentum" and is due to that the FW transformation maps pointlike particles to particle clouds for which the prescription of minimal coupling is incorrect, as they have multipole moments. We express energy and momentum conservation for the system of particles and the electromagnetic field, and discuss our results in the context of the Abraham-Minkowski dilemma.

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“…In this sense, our calculation is also related to that in, e.g., Refs. [19,54,55], but with the following difference. In contrast to other papers, and as we already pointed out in a different context, our theory is constructed straightforwardly by deduction from the quantum LD.…”

Section: Comparison With Other Modelsmentioning

confidence: 99%

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

Ruiz

Dodin

2015

Physics Letters A

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Linear vector waves, both quantum and classical, experience polarization-driven bending of ray trajectories and polarization dynamics that can be interpreted as the precession of the "wave spin". Both phenomena are governed by an effective gauge Hamiltonian, which vanishes in leading-order geometrical optics. This gauge Hamiltonian can be recognized as a generalization of the SternGerlach Hamiltonian that is commonly known for spin-1/2 quantum particles. The corresponding reduced Lagrangians for continuous nondissipative waves and their geometrical-optics rays are derived from the fundamental wave Lagrangian. The resulting Euler-Lagrange equations can describe simultaneous interactions of N resonant modes, where N is arbitrary, and lead to equations for the wave spin, which happens to be a (N 2 −1)-dimensional spin vector. As a special case, classical equations for a Dirac particle (N = 2) are deduced formally, without introducing additional postulates or interpretations, from the Dirac quantum Lagrangian with the Pauli term. The model reproduces the Bargmann-Michel-Telegdi equations with added Stern-Gerlach force.

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Correspondence between classical and Dirac-Pauli spinors in view of the Foldy-Wouthuysen transformation

Cited by 11 publications

References 34 publications

Spin-one-half particles in strong electromagnetic fields: Spin effects and radiation reaction

Spin-one-half particles in strong electromagnetic fields: Spin effects and radiation reaction

Relativistic kinetic equation for spin-1/2 particles in the long-scale-length approximation

Lagrangian geometrical optics of nonadiabatic vector waves and spin particles

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