Riemann Surfaces of Some Static Ispersion Models and Projective Spaces

TL;DR

This paper explores the analytical continuation of the S-matrix in static dispersion models using projective space methods, providing a new approach to understanding complex energy plane behaviors.

Contribution

It introduces a novel method employing projective spaces for the global analysis of nonlinear difference equations related to the S-matrix.

Findings

Effective analysis of the S-matrix continuation in complex energy planes

Application of projective space techniques to dispersion models

Insights into crossing symmetry and matrix relations

Abstract

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.