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Relativistic kinetic equation for spin-1/2 particles in the long-scale-length approximation
Umeå University, Faculty of Science and Technology, Department of Physics.
Umeå University, Faculty of Science and Technology, Department of Physics.
2017 (English)In: Physical review. E, ISSN 2470-0045, E-ISSN 2470-0053, Vol. 96, no 2, 023207Article in journal (Refereed) Published
Abstract [en]

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.

Place, publisher, year, edition, pages
American Physical Society, 2017. Vol. 96, no 2, 023207
National Category
Fusion, Plasma and Space Physics
Identifiers
URN: urn:nbn:se:umu:diva-139142DOI: 10.1103/PhysRevE.96.023207ISI: 000408118100012OAI: oai:DiVA.org:umu-139142DiVA: diva2:1146638
Available from: 2017-10-03 Created: 2017-10-03 Last updated: 2017-10-03Bibliographically approved

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Ekman, RobinZamanian, Jens
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