  We predict that spin-waves in an ordered square quantum antiferromagnet in a
transverse magnetic field (h) may demonstrate three modes of spin excitations.
Starting from the self-consistent rotation-invariant Green's function method, a
new mean-field theory is constructed for h not equal to 0. The method preserves
the translational and the axial symmetries, and provides exact fulfillment of
the single-site constraint for each of the three modes. We examine the
dynamical structure factors S(aa)(k,w), a= x, y, z. It is shown, that the
introduction of h leads to the hybridization of two degenerate spin modes due
to the appearance of a nondiagonal on a, b spin-spin Green's functions. The
comparison of the theory with the exact diagonalization study and with results
on inelastic neutron scattering experiments is discussed at T = 0. We discuss
also the correspondence of the theory to the existing theories, which allow
only two spin excitations modes for the total S(k,w).
