This work is a first step in a program for construction of meson-meson scattering amplitudes with analyticity, crossing symmetry, and unitarity. The construction is to be carried out by solving a nonlinear integral equation for the partial wave amplitude a(l, s) at complex l and physical s. The program is intended to overcome the difficulties encountered in the traditional approach based on the Mandelstam iteration of double-spectral functions. An important initial step is to analyze nonrelativistic potential scattering from this autonomous S-matrix viewpoint, in which the Schrödinger equation is replaced by a nonlinear equation for the partial wave amplitude. In the present paper, it is demonstrated that the partial-wave equation has a locally unique solution, provided the potential is of a suitably restricted Yukawa type. This result indicates the feasibility of a pure S-matrix approach to dynamics. In the present report, the potential is so restricted in strength as to preclude bound states or resonances. The extension of the method to the case of strong potentials will be pursued in a later publication.
|Number of pages||15|
|Journal||Journal of Mathematical Physics|
|Publication status||Published - 1974|