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Physical Review A

Comment on “Relativistic effects on the spin entanglement of two massive Dirac particles”

Paweł Caban, Jakub Rembieliński

Published Dec 26, 2012• 3 citations
Publisher

Abstract

The paper of Choi et al. [Phys. Rev. A 84, 012334 (2011)] discusses the use of the Foldy-Wouthuysen mean-spin operator in the theory of relativistic quantum information. However, the paper contains some incorrect statements and misunderstandings.
DOI
10.1103/physreva.86.066301

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We give a direct link between description of Dirac particles in the abstract framework of unitary representation of the Poincaré group and description with the help of the Dirac equation. In this context we discuss in detail the spin operator for a relativistic Dirac particle. We show also that the spin operator used in quantum field theory for spin s=1/2s=1/2s=1/2 corresponds to the Foldy-Woutheysen mean-spin operator.
The problem of the position and spin in relativistic quantum mechanics is analyzed in detail. It is definitively shown that the position and spin operators in the Foldy-Wouthuysen representation (but not in the Dirac one) are quantum-mechanical counterparts of the classical position and spin variables. The probabilistic interpretation is valid only for Foldy-Wouthuysen wave functions. The relativistic spin operators are discussed. The spin-orbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the rest-frame spin are used. Alternative definitions of the orbital angular momentum and the spin are based on noncommutative geometry, do not satisfy standard commutation relations, and can allow the spin-orbit interaction.