Position, spin, and orbital angular momentum of a relativistic electron

Abstract

General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Motivated by recent interest in relativistic electron vortex states, we revisit the spin and orbital angular momentum properties of Dirac electrons. These are uniquely determined by the choice of the position operator for a relativistic electron. We consider two main approaches discussed in the literature: (i) the projection of operators onto the positive-energy subspace, which removes the Zitterbewegung effects and correctly describes spin-orbit interaction effects, and (ii) the use of Newton-Wigner-Foldy-Wouthuysen operators based on the inverse Foldy-Wouthuysen transformation. We argue that the first approach [previously described in application to Dirac vortex beams in K. Y. Bliokh et al., Phys. Rev. Lett. 107, 174802 (2011)] has a more natural physical interpretation, including spin-orbit interactions and a nonsingular zero-mass limit, than the second one [S. M.

Position and spin in relativistic quantum mechanics

“…III-V. All these results contradict to the key statement in Ref. [95] that the spin is defined by the operator s D = Σ/2 in the Dirac representation.…”

“…(7) in Ref. [95] coinciding with Eq. (75) in the present study has nothing in common with "the Lorentz boost to the rest frame".…”

“…It is also claimed in Ref. [95] that the projected operators are covariant. However, the results obtained in Refs.…”

“…Evidently, the FW mean-spin operator commutes with the FW Hamiltonian (25) In Refs. [94,95,107], the existence of the SOI for a free Dirac particle has been claimed.…”

“…However, our conclusions contradict the conclusions which have been made in Refs. [9,10,28,29,94,95,[104][105][106][107] and are widely used in physics of twisted electrons and relativistic quantum chemistry. The analysis of the latter conclusions launched in this section will be finalized in Sec.…”