Constraints on the momentum dependence of rho-omega mixing

Within a broad class of models we show that the amplitude for rho^0-omega mixing must vanish at the transition from timelike to spacelike four momentum. Hence in such models the mixing is either zero everywhere or is necessarily momentum-dependent. This lends support to the conclusions of other studies of rho-omega mixing and calls into question standard assumptions about the role of rho-omega mixing in the theoretical understanding of charge-symmetry breaking in nuclear systems.