  We study kinetics of single species reactions ("A+A -> 0") for general local
reactivity Q and dynamical exponent z (rms displacement x_t ~ t^{1/z}.) For
small molecules z=2, whilst z=4,8 for certain polymer systems. For dimensions d
above the critical value d_c=z, kinetics are always mean field (MF). Below d_c,
the density n_t initially follows MF decay, n_0 - n_t ~ n_0^2 Q t. A 2-body
diffusion-controlled regime follows for strongly reactive systems (Q>Qstar ~
n_0^{(z-d)/d}) with n_0 - n_t ~ n_0^2 x_t^d. For Q<Qstar, MF kinetics persist,
with n_t ~ 1/Qt. In all cases n_t ~ 1/x_t^d at the longest times. Our analysis
avoids decoupling approximations by instead postulating weak physically
motivated bounds on correlation functions.
