Exact Foldy-Wouthuysen transformation of the Dirac-Pauli Hamiltonian in the weak-field limit by the method of direct perturbation theory

Abstract

We apply the method of direct perturbation theory for the Foldy-Wouthuysen (FW) transformation upon the Dirac-Pauli Hamiltonian subject to external electromagnetic fields. The exact FW transformations exist and agree with those obtained by Eriksen's method for two special cases. In the weak-field limit of static and homogeneous electromagnetic fields, by mathematical induction on the orders of $1/c$ in the power series, we rigorously prove the long-held speculation: the FW transformed Dirac-Pauli Hamiltonian is in full agreement with the classical counterpart, which is the sum of the orbital Hamiltonian for the Lorentz force equation and the spin Hamiltonian for the Thomas-Bargmann-Michel-Telegdi equation.

37 pages; follow-up to arXiv:1311.3432; contains some of the same review materials in arXiv:1310.8513. v4: revised with various improvements; version appears in PRA

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Cited by in corpus (5)

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• Bouncing Dirac particles: compatibility between MIT boundary conditions and Thomas precession
• Leading correction to the relativistic Foldy-Wouthuysen Hamiltonian