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Selfadjoint extensions and scattering theory for several-body systems. (English) Zbl 0756.35064

The aim of this paper is to introduce the main technique used to construct the scattering theory for several-body systems with energy- dependent interactions. Methods that are not traditional in scattering theory of several-particle systems are developed: generalizations of extension theory of symmetric operators using auxiliary Hilbert spaces, boundary value problems for the Laplacians on thin manifolds and higher- layer potential theory on noncompact manifolds. First von Neumann’s extension theory in terms of boundary forms is reformulated and generalized to operators with non-dense domains. Schwartz integral, Krein formula and transport of deficiency subspaces are studied. A family of model selfadjoint Hamiltonians for a two-body system with nontrivial interval structure is constructed and also for the three-body problem.

MSC:

35P25 Scattering theory for PDEs
81U10 \(n\)-body potential quantum scattering theory
47A40 Scattering theory of linear operators
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