The N-Particle Scattering Problem: Asymptotic Completeness for Short-Range Systems

Abstract

We develop an approach to scattering theory for generalized N -body systems. In particular we consider a general class of three quasi-particle systems, for which we prove Asymptotic Completeness.

Tosio Kato’s work on non-relativistic quantum mechanics: part 2

“…We note that the earliest proofs of N -body asymptotic completeness for 0(|x| −1− ) potentials (at least when N ≥ 4) were by Sigal-Soffer [564,565] and then by Graf [196] and Dereziński [115]. Dereziński [115] and Sigal and Soffer [565] have results on long range results.…”

Asymptotic Completeness for Four-Body Schrödinger Operators with Short-Range Interactions

“…Besides the work [13], there are many works dealing with the problem of asymptotic completeness for many-body systems. An extensive list of related references can be found in [2] and [13].…”

“…In particular, the proof does not have required a phase space partition of unity with the property that the boundaries of its support lie in the classically forbidden region. The construction of such a phase space partition of unity is one of the most essential steps in the original proof by [13], The aim of this work is to develope further the argument used in [15] to prove the asymptotic completeness for four-body systems with short-range pair interactions. The author hopes that the previous and present works reveal the difficulties to be overcome in the future study towards proving the asymptotic completeness for general Nbody, 7V;>5, systems.…”

“…The proof in [15] has been in principle based on the same idea as in [13] but several new ingredients have been added to the techniques developed there. In particular, the proof does not have required a phase space partition of unity with the property that the boundaries of its support lie in the classically forbidden region.…”

Propagation estimates for Dirac operators and application to scattering theory

“…In particular, Sigal and Soffer [30], [31], Graf [18] and Derezinski and Gérard [8] improved the methods of Enss The notion of strong-Coo-limit is explained at the beginning of Section 5. The asymptotic velocity admits the other characterization in terms of the classical velocity operator V and we see that (1.2) together with (1.3) imply (1.1).…”