1999/10/06 by András Vasy, Andras Vasy, Vasy, Andras · 1 citation
Mathematics · Physics and Astronomy · #35P25 (Primary) 47A40 #58G25 #81U10 (Secondary) #Analysis of PDEs (math.AP) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum optics and atomic interactions #Spectral Theory in Mathematical Physics #math-ph #math.AP #math.MP #msc:35P25 #msc:47A40 #msc:58G25 #msc:81U10
paper · pdf · doi:10.48550/arxiv.math/9910033
68 pages; AMS Latex
arxiv created 1999/10/06 · openalex publication_date 1999/10/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We describe the propagation of singularities of tempered distributional generalized eigenfunctions of many-body Hamiltonians at non-threshold energies under the assumption that the inter-particle interactions are real-valued polyhomogeneous symbols of order -1 (e.g. Coulomb-type, but without the singularity at the origin). Here the term `singularity' refers to a microlocal description of the lack of decay at infinity. We use this result to describe the wave front relation of the S-matrices. We also analyze Lagrangian properties of this relation, which shows that the relation is not `too large' in terms of its dimension.