Exakte Lösungen von Low-Gleichungen

Abstract

The general solution of the Low equation for a family of two-dimensional crossingmatrices is constructed. It depends on 2 arbitrary functions and its Riemann surface has an infinity of distinct sheets. Furthermore a subclass of solutions of the 3dimensional and 4dimensional pseudoscalar symmetricπ-N scattering theory is constructed, the former depending on 2 arbitrary functions, the latter on 3. The criterion of minimal zeros in the scattering functions on the physical sheet is applied, to restrict this manyfold. In the threedimensional case the restricted solution depends on 2 parameters which may be interpreted as “coupling constant” and “cut off”. In the 4dimensional case the criterion of minimal zeros in the scattering functions gives a solution which depends on 5 parameters and thus is not uniquely determined by a “coupling constant” and a “cut off”.