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

摘要

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