Mehrfache Dispersionsrelationen für kurzreichweitige Potentiale, die sich nicht durch eine Überlagerung von Yukawa-Potentialen darstellen lassen

Abstract

A triple dispersion relation is derived for the functionf(s, t, u) which becomes the scattering amplitudef(s, t) foru=4s−t. Besides the usual conditions which are needed for deriving a dispersion relation ins, the potential must decrease faster than exponentially at infinity. For this class of potentialsf(s, t, u) has essential singularities fort→∞ andu→∞. It is shown thatf(s, t, u) is bounded in the physical sheets of two independent Riemannian surfaces which are constructed by conformal mappings of thet- and theu-plane. In the new variables the conditions for the existence of dispersion relations are fulfilled.