Position and spin in relativistic quantum mechanics
Abstract
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 FoldyWouthuysen representation (but not in the Dirac one) are quantummechanical counterparts of the classical position and spin variables. The probabilistic interpretation is valid only for FoldyWouthuysen wave functions. The relativistic spin operators are discussed. The spinorbit interaction does not exist for a free particle if the conventional operators of the orbital angular momentum and the restframe 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 spinorbit interaction.
 Publication:

Physical Review A
 Pub Date:
 March 2020
 DOI:
 10.1103/PhysRevA.101.032117
 arXiv:
 arXiv:2003.06572
 Bibcode:
 2020PhRvA.101c2117Z
 Keywords:

 Quantum Physics
 EPrint:
 46 pages, no figure