2005/11/28 by Alexander K. Motovilov, А. К. Мотовилов
Materials Science · Mathematics · Physics and Astronomy · #Magnetism in coordination complexes #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #math-ph #math.MP #nucl-th #physics.atm-clus
paper · pdf · doi:10.1007/s00601-005-0134-y
published as Few Body Systems, Vol. 38 (2006) 115-120 · Based on a lecture given at the International Workshop ``Critical Stability of Few-Body Quantum Systems'' (Dresden, October 17--22, 2005)
arxiv created 2005/11/28 · openalex publication_date 2006/04/26 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We discuss the structure of the two- and three-body T-matrices, scattering matrices, and resolvents continued to the unphysical energy sheets. Our conclusions arise due to the representations that have been found for analytically continued momentum-space kernels of the T-operators. These representations are explicitly written only in terms of the physical-sheet kernels of the T-matrix itself. One of advantages of the representations in the three-body case is that they show which portions of the physical-sheet three-body scattering matrix are ``responsible'' for the resonances associated with a particular unphysical sheet. A resonance appears to be the energy where the correspondingly truncated scattering matrix (taken on the physical sheet) has eigenvalue zero. We also mention applications of this approach to some specific three-body systems, based on the Faddeev differential equations.