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.
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Die Verfasser danken Herrn Professor Dr. F.Schlögl und Herrn Dr. R.Bausch für die Anregung zu dieser Arbeit und zahlreiche Diskussionen.
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Günther, U., Janssen, H.K. Mehrfache Dispersionsrelationen für kurzreichweitige Potentiale, die sich nicht durch eine Überlagerung von Yukawa-Potentialen darstellen lassen. Z. Physik 200, 366–374 (1967). https://doi.org/10.1007/BF01326178
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DOI: https://doi.org/10.1007/BF01326178