Asymptotic completeness for short-range N-body systems revisited

TL;DR

This paper revisits Yafaev's approach to proving asymptotic completeness in short-range N-body quantum systems, emphasizing commutator methods and Kato smoothness bounds.

Contribution

It provides a detailed review and possibly new insights into Yafaev's method for establishing asymptotic completeness in short-range N-body systems.

Findings

Clarifies the role of commutator estimates in asymptotic completeness

Highlights the importance of Kato smoothness bounds in the analysis

Reinforces the effectiveness of Yafaev's approach for short-range interactions

Abstract

We review Yafaev's approach to asymptotic completeness for systems of particles mutually interacting with short-range potentials. The theory is based on computation of commutators with time-independent (mostly bounded) observables yielding a sufficient supply of Kato smoothness bounds.