Mathematical Surveys and Monographs 2002; 242 pp; hardcover Volume: 90 ISBN10: 082182919X ISBN13: 9780821829196 List Price: US$74 Member Price: US$59.20 Order Code: SURV/90
 This monograph offers a rigorous mathematical treatment of the scattering theory of quantum Nparticle systems in an external constant magnetic field. In particular, it addresses the question of asymptotic completeness, a classification of all possible trajectories of such systems according to their asymptotic behavior. The book adopts the socalled timedependent approach to scattering theory, which relies on a direct study of the Schrödinger unitary group for large times. The modern methods of spectral and scattering theory introduced in the 1980s and 1990s, including the Mourre theory of positive commutators, propagation estimates, and geometrical techniques, are presented and heavily used. Additionally, new methods were developed by the authors in order to deal with the (much less understood) phenomena due to the presence of the magnetic field. The book is a good starting point for graduate students and researchers in mathematical physics who wish to move into this area of research. It includes expository material, research work previously available only in the form of journal articles, as well as some new unpublished results. The treatment of the subject is comprehensive and largely selfcontained, and the text is carefully written with attention to detail. Readership Graduate students and research mathematicians interested in mathematical physics and differential equations. Reviews "The book is well organized and well written ... the authors have successfully achieved their stated aim of writing a book which is of interest both to a wider section of the mathematical physics community ... and to graduate students and researchers in the field of spectral and scattering theory for magnetic Schrödinger operators."  Mathematical Reviews Table of Contents  Fundamentals
 Geometrical methods I
 The Mourre theory
 Basic propagation estimates
 Geometrical methods II
 Wave operators and scattering theory
 Open problems
 Appendix
 Bibliography
 Index
