  We formulate the dynamics of local order parameters by extending the recently
developed adiabatic spinwave theory involving the Berry curvature, and derive a
formula showing explicitly the role of the Berry phase in determining the
spectral form of the low-lying collective modes. For antiferromagnetic spin
chains, the Berry phase becomes a topological invariant known as the Chern
number. Our theory predicts the existence of the Haldane gap for a
topologically trivial ground state, and a linear dispersion of low-lying
excitations for a non-trivial ground state.
