Gell-Mann-Low equation and on-mass-shell amplitudes

We show how, in certain theories, the Gell-Mann-Low renormalization-group equation can be applied to physical on-mass-shell amplitudes. These theories are characterized by a selection rule softening the zero-mass singularities in external mass channels. Physical amplitudes asymptotically reflect the anomalous dimensions of the theory. In particular, this analysis provides a field-theoretical argument for a connection between the asymptotic behavior of elastic amplitudes at fixed angle and the electromagnetic form factors. This connection is similar to that proposed by Wu and Yang.