  Nonrelativistic bound states are studied using an effective field theory.
Large logarithms in the effective theory can be summed using the velocity
renormalization group. For QED, one can determine the structure of the leading
and next-to-leading order series for the energy, and compute corrections up to
order alpha^8 ln^3 alpha, which are relevant for the present comparison between
theory and experiment. For QCD, one can compute the velocity renormalization
group improved quark potentials. Using these to compute the renormalization
group improved t-tbar production cross-section near threshold gives a result
with scale uncertainties of 2%, a factor of 10 smaller than existing fixed
order calculations.
