Relativistic kinetic equation for spin-1/2 particles in the long-scale-length approximation
Ekman
R
author
Asenjo
F
A
author
Zamanian
J
author
2017
English
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 (h) over bar. 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.
WOS:000408118100012
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text
files/759_Ekman_etal2017.pdf
10.1103/PhysRevE.96.023207
Ekman_etal2017
Physical Review E
Phys. Rev. E
2017
Amer Physical Soc
continuing
periodical
academic journal
96
2
8 pp
2470-0045