  In the framework of vector model of spin, we discuss the problem of a
covariant formalism \cite{Pomeranskii1998} concerning the discrepancy between
relativistic and Pauli Hamiltonians. We show how the spin-induced non
commutativity of a position accounts the discrepancy on the classical level,
without appeal to the Dirac equation and Foldy-Wouthuysen transformation.
