Mathematical theory of single channel systems. Analyticity of scattering matrix

Abstract

We show that the S S -matrix of a quantum many-body, short-range, single-channel system has a meromorphic continuation whose poles occur at most at the dilation-analytic resonances [28], [24] and at the eigenvalues of the Hamiltonian. In passing, we prove the main spectral theorem (on location of the essential spectrum) and asymptotic completeness for the mentioned class of systems.