Riemann Surfaces of Some Static Ispersion Models and Projective Spaces

The S-matrix in the static limit of a dispersion relation has a finite order N and is a matrix of meromorfic functions of energy in the complex plane with cuts. In the elastic case it reduces to N functions connected by the crossing symmetry matrix A. The problem of analytical continuation of S - matrix from the physical sheet to unphysical ones can be treated as a nonlinear system of difference equations. It is shown that a global analisis of this system can be carried out effectively in projective spaces. Some applications of the method used are considered.