  The interaction of the electric and magnetic dipole moments of a particle
with the electromagnetic field is investigated in an approach that deals with
four-dimensional (4D) geometric quantities. The new commutation relations for
the 4D orbital and intrinsic angular momentums and also for the 4D dipole
moments are introduced. The expectation value of the quantum 4-force, which
holds in any frame, is worked out in terms of them. In contrast to it the whole
calculation in [1] ([1] J. Anandan, Phys. Rev. Lett. \textbf{85}, 1354 (2000))
has been made only in the rest frame of the dipole. It is proved that, e.g.,
the expression for the 3D force $\mathbf{f}%_{S}$ in [1] is not
relativistically correct and that the quantum 4-force is not zero in the
experiments proposed in [1]. This means that the phase shifts that could be
observed in such experiments are not topological phase shifts.
