Relativistic Transport Equations for Electromagnetic, Scalar, and Pseudoscalar Potentials

Shin, Ghi Ryang; Rafelski, Johann

doi:10.1006/aphy.1995.1090

Cited by 13 publications

(21 citation statements)

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“…The alternative approach is to use the equaltime Wigner function [43] which breaks explicitly the Lorentz covariance because the Fourier transform with respect to the relative time coordinate is not performed. However, such an equal-time Wigner function poses a mathematically well-defined initial-value problem and its interpretation as a quasiprobability distribution function in the phase space is physically transparent [43,44,61,62]. [Note that the Wigner function is a quasiprobability distribution function because it can take negative values].…”

Section: Wigner Function In a Constant Magnetic Fieldmentioning

confidence: 99%

Wigner function and kinetic phenomena for chiral plasma in a strong magnetic field

Gorbar

Miransky

Shovkovy

et al. 2017

J. High Energ. Phys.

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By using the exact solutions of the Weyl equation in a constant magnetic field, the equal-time Wigner function for magnetized chiral plasma is derived. It is found that the dependence of the Wigner function on the component of momentum along the magnetic field is asymmetric and is correlated with the fermion chirality. Such a dependence is principal for reproducing the correct chiral magnetic and chiral separation effects. In the lowest Landau level approximation, the equation for the equal-time Wigner function in a strong magnetic field is derived. By making use of this equation, it is found that the longitudinal collective modes in a strong magnetic field are gapped plasmons whose gap is determined by the magnetic field. Unlike the ordinary magnetic field, an axial one allows for the dispersion law of the collective excitations asymmetric in the wave vector. The thermoelectric phenomena for chiral fermions in strong magnetic and axial magnetic fields are studied and the corresponding transport coefficients are calculated.

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Section: Wigner Function In a Constant Magnetic Fieldmentioning

confidence: 99%

Wigner function and kinetic phenomena for chiral plasma in a strong magnetic field

Gorbar

Miransky

Shovkovy

et al. 2017

J. High Energ. Phys.

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“…The basic tool in this formalism is the 16-component Dirac-HeisenbergWigner (DHW) function. The formalism based on the DHW function was further developed in [2][3][4][5] to yield quantum transport theory for relativistic spinning particles. In several papers [6][7][8][9][10][11] a relativistic generalization of the Wigner function was introduced.…”

Section: Introductionmentioning

confidence: 99%

Time evolution of the QED vacuum in a uniform electric field: Complete analytic solution by spinorial decomposition

Bialynicki‐Birula

Rudnicki

2011

Phys. Rev. D

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Exact analytical solutions are presented for the time evolution of the density of pairs produced in the QED vacuum by a time-independent, uniform electric field. The mathematical tool used here to describe the pair production is the Dirac-Heisenberg-Wigner function introduced before [Phys. Rev. D 44, 1825]. The initial value problem for this function is solved by decomposing the solution into a product of spinors. The equations for spinors are much simpler and are solved analytically. These calculations are nonperturbative since pair production is due to quantum-mechanical tunneling and the explicit solutions clearly exhibit their nonanalytic behavior.

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“…What intrigued us was the assertion [4] that the 'derivation' leads to the Dirac equation, instead of to the Klein-Gordon equation. To examine this question more closely, we were led to start from the opposite direction to [4], viz., a 'direct' derivation of the Liouville equation through an explicit construction of the Wigner Functions [7] themselves, as in more orthodox approaches [5,6], with a view to throwing some light on this apparent asymmetry between the Dirac and the K-G cases. Rather surprisingly, our result indicates a close parallelism between both spin-1/2 and spin-(0,1) cases, brought about by the Kemmer-Duffin [8] formalism [13] for integral spin as a natural counterpart to the Dirac equation for spin-1/2.…”

Section: Discussionmentioning

confidence: 99%

On simulating Liouvillian flow from quantum mechanics via Wigner functions

Mitra¹,

Ramanathan

1998

Journal of Mathematical Physics

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The interconnection between quantum mechanics and probabilistic classical mechanics for a free relativistic particle is derived in terms of Wigner functions (WF) for both Dirac and Klein-Gordon (K-G) equations. Construction of WF is achieved by first defining a bilocal 4-current and then taking its Fourier transform w.r.t. the relative 4-coordinate. The K-G and Proca cases also lend themselves to a closely parallel treatment provided the Kemmer-Duffin β-matrix formalism is employed for the former. Calculation of WF is carried out in a Lorentz-covariant fashion by standard 'trace' techniques. The results are compared with a recent derivation due to Bosanac.

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Relativistic Transport Equations for Electromagnetic, Scalar, and Pseudoscalar Potentials

Cited by 13 publications

References 0 publications

Wigner function and kinetic phenomena for chiral plasma in a strong magnetic field

Wigner function and kinetic phenomena for chiral plasma in a strong magnetic field

Time evolution of the QED vacuum in a uniform electric field: Complete analytic solution by spinorial decomposition

On simulating Liouvillian flow from quantum mechanics via Wigner functions

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