C0-Groups, Commutator Methods and Spectral Theory of N-Body Hamiltonians

Second revised edition
1. Auflage 1996
ISBN: 978-3-7643-5365-0
Verlag: Springer

Buch, Englisch, Band 135, 464 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 1880 g

Reihe: Progress in Mathematics

The relevance of commutator methods in spectral and scattering theory has been known for a long time, and numerous interesting results have been ob­ tained by such methods. The reader may find a description and references in the books by Putnam [Pu], Reed-Simon [RS] and Baumgartel-Wollenberg [BW] for example. A new point of view emerged around 1979 with the work of E. Mourre in which the method of locally conjugate operators was introduced. His idea proved to be remarkably fruitful in establishing detailed spectral properties of N-body Hamiltonians. A problem that was considered extremely difficult be­ fore that time, the proof of the absence of a singularly continuous spectrum for such operators, was then solved in a rather straightforward manner (by E. Mourre himself for N = 3 and by P. Perry, 1. Sigal and B. Simon for general N). The Mourre estimate, which is the main input of the method, also has consequences concerning the behaviour of N-body systems at large times. A deeper study of such propagation properties allowed 1. Sigal and A. Soffer in 1985 to prove existence and completeness of wave operators for N-body systems with short range interactions without implicit conditions on the potentials (for N = 3, similar results were obtained before by means of purely time-dependent methods by V. Enss and by K. Sinha, M. Krishna and P. Muthuramalingam). Our interest in commutator methods was raised by the major achievements mentioned above.

Zielgruppe

Research

Autoren/Hrsg.

Amrein, Werner

Boutet de Monvel, Anne

Georgescu, Vladimir

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Homologische Algebra
• Mathematik | Informatik Mathematik Mathematische Analysis Elementare Analysis und Allgemeine Begriffe
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

1 Some Spaces of Functions and Distributions.- 2 Real Interpolation of Banach Spaces.- 3 C0-Groups and Functional Calculi.- 4 Some Examples of C0-Groups.- 5 Automorphisms Associated to C0-Representations.- 6 Unitary Representations and Regularity.- 7 The Conjugate Operator Method.- 8 An Algebraic Framework for the Many-Body Problem.- 9 Spectral Theory of N-Body Hamiltonians.- 10 Quantum-Mechanical N-Body Systems.- Notations.