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Open Systems & Information Dynamics

Covariant Abstract Description for a Dirac Particle

Paweł Caban, Jakub Rembieliński, Marta Włodarczyk

Published Dec 1, 2012• 4 citations
Publisher

Abstract

We give a direct link between covariant 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 the spin operator for a relativistic Dirac particle. We show also that the spin operator used in quantum field theory for spin s = 1/2 corresponds to the Foldy-Wouthuysen mean-spin operator. We hope that this formalism will be useful in the theory of relativistic quantum information.

DOI
10.1142/s1230161212500278

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We give a direct link between covariant 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 the spin operator for a relativistic Dirac particle. We show also that the spin operator used in quantum field theory for spin s = 1/2 corresponds to the Foldy-Wouthuysen mean-spin operator. We hope that this formalism will be useful in the theory of relativistic quantum information.
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.