Classical Many-Body Problems Amenable to Exact Treatments

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

Francesco Calogero (Autor)

Buch | Softcover

XVIII, 749 Seiten

2014 | 2001
Springer Berlin (Verlag)
978-3-662-14344-5 (ISBN)

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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).

Classical (Nonquantal, Nonrelativistic) Many-Body Problems.- One-Dimensional Systems. Motions on the Line and on the Circle.- N-Body Problems Treatable Via Techniques of Exact Lagrangian Interpolation in Space of One or More Dimensions.- Solvable and/or Integrable Many-Body Problems in the Plane, Obtained by Complexification.- Many-Body Systems in Ordinary (Three-Dimensional) Space: Solvable, Integrable, Linearizable Problems.- Appendices: A: Elliptic Functions.- B: Functional Equations.- C: Hermite Polynomials.- D: Remarkable Matrices and Related Identities.- E: Langrangian Approximation for Eigenvalue Problems in One and More Dimensions.- F: Some Theorems of Elementary Geometry in Multidimensions.- G: Asymptotic Behavior of the Zeros of a Polynomial Whose Coefficients Diverge Exponentially.- H: Some Formulas for Pauli Matrices and Three-Vectors.- References.

"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)

Erscheint lt. Verlag	23.8.2014
Reihe/Serie	Lecture Notes in Physics Monographs
Zusatzinfo	XVIII, 749 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	1140 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Allgemeines / Lexika
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Theoretische Physik
Schlagworte	Dynamical system • Geometry • Hamiltonian Many-Body Problem • Lax Pair • Liouville Solvability
ISBN-10	3-662-14344-5 / 3662143445
ISBN-13	978-3-662-14344-5 / 9783662143445
Zustand	Neuware