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Bound States in NRQCD/NRQED and the Renormalization Group

The application of renormalization group techniques to bound states in non-relativistic QED and QCD is discussed. For QED bound states like Hydrogen and positronium, the renormalization group allows large logarithms of the velocity, ln v (or equivalently ln alpha's), to be predicted in a universal and simple way. The series of (alpha ln alpha)'s are shown to terminate after a few terms. For QCD one can systematically sum infinite series of the form [alpha_s ln alpha_s]^k$, and answer definitively the question ``alpha_s at what scale?''.