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It has long been speculated that the Dirac or, more generally, theDirac-Pauli spinor in the Foldy-Wouthuysen (FW) representation should behavelike a classical relativistic spinor in the low-energy limit when theprobability of particle-antiparticle pair creation and annihilation isnegligible. In the weak-field limit of static and homogeneous electromagneticfields, by applying the method of direct perturbation theory inductively on theorders of $1/c$ in the power series, we rigorously prove that it is indeed thecase: the FW transformation of the 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.

Exact correspondence between classical and Dirac-Pauli spinors in the weak-field limit of static and homogeneous electromagnetic fields