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

Kuperin, Yu. A.; Merkur’ev, S. P.

Transl., Ser. 2, Am. Math. Soc. 150, 141-176 (1992).

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.

Reviewer: K.Hardenberg (Braunschweig)

MSC:

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

Keywords:

systems with energy-dependent interactions; Schwartz integral; Krein formula