Bootstrap of theρRegge Trajectory

Abstract

The amplitude for $\omega +\pi \to \pi +\pi$ is considered within a dynamical scheme proposed by Mandelstam, based on rising Regge trajectories, the narrow-resonance approximation, and generalized superconvergence relations. The $\rho$ trajectory is shown to qualitatively bootstrap itself. Also, a world consisting only of the particles on a vacuum trajectory is shown to be inconsistent within this approximation.