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