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Scattering theory of classical and quantum \(N\)-particle systems. (English) Zbl 0899.47007
Texts and Monographs in Physics. Berlin: Springer. xii,444 p. (1997).
Dereziński and Gérard present the scattering theory of one particle (‘two-body’ in the dialect of scattering theorists) and several particles, a topic that was one of the prime areas of research in mathematical physics during the last years. The book is a comprehensive and largely self-contained introduction that includes major recent developments up to 1996 including the asymptotic completeness in \(N\)-body quantum case with long range potentials. [The first proof of this fact was given by the first author, Ann. Math., II. Ser. 138, No. 2, 427-476 (1993; Zbl 0844.47005)]. The book is very well written; also a non-expert in scattering theory is able to follow the arguments. Although there is some emphasis on the quantum part of scattering theory, the two main chapters on one-particle and many-particle quantum scattering theory are preceded by corresponding sections on classical scattering, a concept that helps to develop the intuition and clearly enhances the understanding of the sections on quantum scattering as well.

47A40 Scattering theory of linear operators
81U10 \(n\)-body potential quantum scattering theory
81U05 \(2\)-body potential quantum scattering theory
47-02 Research exposition (monographs, survey articles) pertaining to operator theory
81-02 Research exposition (monographs, survey articles) pertaining to quantum theory