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Classical Many-Body Problems Amenable to Exact Treatments

(Solvable and/or Integrable and/or Linearizable...) in One-, Two- and Three-Dimensional Space

  • Book
  • © 2001

Overview

Authors:
  1. Francesco Calogero

    1. Department of Physics, University of Rome “La Sapienza”, Roma, Italy

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  • One of the leading experts presents a host of new results in a form accessible to graduates
  • Many examples and problems make this a real workbook for the interested reader from physics as well as mathematics
  • Includes supplementary material: sn.pub/extras

Part of the book series: Lecture Notes in Physics Monographs (LNPMGR, volume 66)

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About this book

This book focuses treatable This class on exactly many' body problems. does not include most We are therefore reminded "of physical problems. the of the man home late at after an alcoholic who, story returning night the for his under he was a knew, evening, scanning ground key lamppost; be that he had it somewhere but under the to sure, dropped else, only Yet was there to conduct a searcW' . light lamppost enough proper we feel the interest for such models is nowadays sufficiently widespread because of their their mathematical relevance and their multi beauty, farious that need be made for no our apologies applicative potential choice. In whoever undertakes to read this book will know from any case, its title what she is in for! Yet this title a of it some may require explanations: gloss (including its extended inside front follows. version, see cover) and nonrelativistic "Classical" we mean nonquantal (although By consider the which indeed some are Ruijsenaars Schneider models, treated in this relativistic versions as known, nonre book, of, previously lativistic is focussed see our on models; below): presentation mainly of whose time evolution is determined many body point particles systems Newtonian of motion to by equations (acceleration proportional force).

Keywords

Table of contents (5 chapters)

  1. Front Matter

    Pages I-XVIII
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  2. Classical (Nonquantal, Nonrelativistic) Many-Body Problems

    Pages 1-16

  3. One-Dimensional Systems - Motions on The Line and on The Circle

    Pages 17-309

  4. N-Body Problems Treatable Via Techniques of Exact Lagrangian Interpolation in Spaces of One or More Dimensions

    Pages 311-415

  5. Solvable and/or Integrable Many-Body Problems in The Plane, Obtained by Complexification

    Pages 417-510

  6. Many-Body Systems in Ordinary (Three-Dimensional) Space: Solvable, Integrable, Linearizable Problems

    Pages 511-662

  7. Back Matter

    Pages 663-749
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Reviews

"The book is built in a multilayer (or ‘telescoped’, in the authors words) structure, with a very rich index: by looking through the table of contents the reader will easily locate the sections in which a given topic or example is dealt with. Inside each section, a similar structure is present, with a very rich supply of more detailed discussions, remarks, problems and exercises; all of this material is set in different types, so that one can easily navigate through the main line of the book and enter the detail only if and where desired. This will help the reader facing such a complete treatment, both in case of students trying to master the subject through a structured study, and in that of practitioners interested in some specific systems. The book is, in the reviewer’s opinion, well suited to both of these uses." (Zentralblatt MATH, 1011, 2003)

"A great attention to all details of calculations [...] allows an undergraduate student or just a novice to follow them. Thus, the book combines the features of a scientific monograph and a textbook (or even the syllabus of a special university course). [...] All in all, the book describes part of the modern theory of integrable systems of classical mechanics as seen by one of its creators. It is highly accessible and will serve as a standard reference for a long time." (Mathematical Reviews 2003a)

Authors and Affiliations

  • Department of Physics, University of Rome “La Sapienza”, Roma, Italy

    Francesco Calogero

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