Connections and Effective S-Matrix in Triangle Representation for Quantum Scattering

Abstract

For quantum few-body systems, a method of spectral representation generated by specially extracted sub-Hamiltonians is developed. In this approach, the connections between the geometry of a base manifold, the spectral structure of sub-Hamiltonians, and the geometric characteristics of induced Hilbert bundles arc investigated. The appropriate relations between connections on these Hilbert bundles and global invariants of S-matrix are obtained. Some applications of the proposed approach to exactly solvable two- and three-body scattering problems are considered.