TY - JOUR

T1 - Relativistic kinetic equation for spin-1/2 particles in the long-scale-length approximation

AU - Ekman, R.

AU - Asenjo, F. A.

AU - Zamanian, J.

N1 - Funding Information:
The authors are grateful for helpful email correspondence with A. J. Silenko, and to two anonymous referees for providing comments that helped improve the paper. R.E. was supported by by the Swedish Research Council, Grant No. 2012-3320. J.Z. acknowledges financial support from the Knut and Alice Wallenberg Foundation within the grant “Plasma based compact ion sources” (PLIONA).
Publisher Copyright:
© 2017 American Physical Society.

PY - 2017/8/22

Y1 - 2017/8/22

N2 - 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 quasidistribution 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 nontrivially 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.

AB - 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 quasidistribution 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 nontrivially 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.

UR - http://www.scopus.com/inward/record.url?scp=85028894137&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.96.023207

DO - 10.1103/PhysRevE.96.023207

M3 - Article

C2 - 28950623

AN - SCOPUS:85028894137

SN - 1539-3755

VL - 96

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

IS - 2

M1 - 023207

ER -