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Nuovo cimento della Società italiana di fisica. A, Nuclei, particles and fields

Remarks on the localization of Dirac particles

Bernd Thaller, Sigrid Thaller

Published Jul 1, 1984• 13 citations
Publisher
DOI
10.1007/bf02782805

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It was known that a free, non-relativistic particle in a superposition of positive momenta can, in certain cases, bear a negative probability current — hence termed quantum backflow. Here, it is shown that more variations can be brought about for a free Dirac particle, particularly when negative-energy solutions are taken into account. Since any Dirac particle can be understood as an antiparticle that acts oppositely (and vice versa), quantum backflow is found to arise in the superposition (i) of a well-defined momentum but different signs of energies, or more remarkably (ii) of different signs of both momenta and energies. Neither of these cases has a counterpart in non-relativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.
Much of the lore of the Zitterbewegung of a free Dirac particle is found to need revision for the situation when the particle is initially localized. We find that in this case the rapid violent oscillations of angular frequency ∠2mc2/h/ in the average position of the particle are a transient rather than sustained phenomenon. Instead, the Zitterbewegung is manifested by a growth in the size of the particle but this growth is many orders of magnitude smaller than h//mc, the magnitude usually quoted. This behavior is contrasted with that of the Foldy-Wouthuysen position for which the Zitterbewegung is absent. Finally, the applicability of these ideas to the situation of a localized Dirac particle in an external field is commented on.