  The spin wave dispersion relation in both clean and disordered itinerant
quantum ferromagnets is calculated. It is found that effects akin to
weak-localization physics cause the frequency of the spin-waves to be a
nonanalytic function of the magnetization m. For low frequencies \Omega, small
wavevectors k, and small m, the dispersion relation is found to be of the form
\Omega ~ m^{1-\alpha} k^2, with \alpha = (4-d)/2 (2<d<4) for disordered
systems, and \alpha = (3-d) (1<d<3) for clean ones. In d=4 (disordered) and d=3
(clean), \Omega ~ m ln(1/m) k^2. Experiments to test these predictions are
proposed.
