Further Remarks on the Impossibility of a Scalar-Meson "Bootstrap"

Abstract

Some lacunae in our previous argument that a single particle can not form a self-sustaining or "boot-strap" system are filled. We propose a method of treating the "potential" that reconciles the Mandelstam iteration procedure with the Regge asymptotic behavior of the double spectral function, by making a subtraction of the $S$-wave discontinuity. This leads to a more general argument that unitarity and crossing symmetry put a very stringent limit on the magnitude of the coupling strength, and exclude the possibility of even producing the bound state corresponding to the particle.