New Criterion for Non-Oscillating High-Energy Behavior of Scattering Amplitudes

A new definition of "non-oscillating" behavior at infinity is proposed which in fact allows for not-too-violent oscillations in the asymptotic region. Assuming that the absorptive part of the scattering amplitudes satisfies it, we show from dispersion relations that the whole amplitude does not oscillate, and from here we rederive, in a general framework, the standard high-energy results, among them, Regge-type behavior (including signature), asymptotic equality of differential cross sections for $A+B$ and $A+\overline{B}$ elastic collisions, and the Pomeranchuk theorem, for a large class of scattering amplitudes.