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Relativistic corrections to the algebra of position variables and spin-orbital interaction. (English) Zbl 1368.81103
Summary: In the framework of vector model of spin, we discuss the problem of a covariant formalism [A. A. Pomeranskii and I. B. Khriplovich, “Equations of motion of a spinning relativistic particle in external fields”, J. Exp. Theor. Phys. 86, No. 5, 839–849 (1998; doi:10.1134/1.558554)] concerning the discrepancy between relativistic and Pauli Hamiltonians. We show how the spin-induced non-commutativity of a position accounts for the discrepancy on the classical level, without appeal to the Dirac equation and Foldy-Wouthuysen transformation.

MSC:
81R15 Operator algebra methods applied to problems in quantum theory
70H45 Constrained dynamics, Dirac’s theory of constraints
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