  We derive the effective long-wavelength Euclidean action for the
antiferromagnetic spin-waves of ordered quantum antiferromagnets subject to a
uniform magnetic field. We point out that the magnetic field dependence of the
spin-wave dispersion predicted by the usual O(3)-quantum nonlinear sigma model
disagrees with spin-wave theory. We argue that the nonlinear sigma model does
not take into account all relevant spin-wave interactions and derive a modified
effective action for the long-wavelength spin-waves which contains an
additional quartic interaction. At zero temperature the corresponding vertex is
relevant in the renormalization group sense below three dimensions.
