Quantum backflow in solutions to the Dirac equation of the spin-$1/2$ free particle

TL;DR

This paper explores quantum backflow phenomena in relativistic spin-1/2 particles described by the Dirac equation, revealing new effects due to negative-energy solutions and superpositions of different momenta and energies.

Contribution

It demonstrates novel quantum backflow effects in Dirac particles, especially involving negative-energy states, extending nonrelativistic concepts to relativistic quantum mechanics.

Findings

Quantum backflow occurs in superpositions of different signs of momenta and energies.

Negative-energy solutions introduce new backflow phenomena not seen in nonrelativistic cases.

A field-theoretic generalization of the backflow effect is also discussed.

Abstract

It was known that a free, nonrelativistic 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 counterpart in nonrelativistic quantum mechanics. A generalization by using the field-theoretic formalism is also presented and discussed.