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Calogero—Moser— Sutherland Models

  • Book
  • © 2000

Overview

Editors:
  1. Jan Felipe Diejen

    1. Departamento de Matematicas, Universidad de Chile, Nunoa Santiago, Chile

  2. Luc Vinet

    1. McGill University, Montreal, Canada

Part of the book series: CRM Series in Mathematical Physics (CRM)

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About this book

In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable. Until then, there was only one known nontrivial example of an exactly solvable quantum multi-particle problem. J. Moser subsequently showed that the classical counterparts to these models is also amenable to an exact analytical approach. The last decade has witnessed a true explosion of activities involving Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical physics (such as soliton theory, quantum field theory, string theory, solvable models of statistical mechanics, condensed matter physics, and quantum chaos) to pure mathematics (such as representation theory, harmonic analysis, theory of special functions, combinatorics of symmetric functions, dynamical systems, random matrix theory, and complex geometry). The aim of this volume is to provide an overview of the many branches into which research on CMS systems has diversified in recent years. The contributions are by leading researchers from various disciplines in whose work CMS systems appear, either as the topic of investigation itself or as a tool for further applications.

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Table of contents (36 chapters)

  1. Front Matter

    Pages i-xxv
    Download chapter PDF

  2. Classical Dynamical r-Matrices for Calogero—Moser Systems and Their Generalizations

    • J. Avan
    Pages 1-21

  3. Hidden Algebraic Structure of the Calogero—Sutherland Model, Integral Formula for Jack Polynomial and Their Relativistic Analog

    • Hidetoshi Awata
    Pages 23-35

  4. Polynomial Eigenfunctions of the Calogero—Sutherland—Moser Models with Exchange Terms

    • T. H. Baker, C. F. Dunkl, P. J. Forrester
    Pages 37-51

  5. The Theory of Lacunas and Quantum Integrable Systems

    • Yuri Yu. Berest
    Pages 53-64

  6. Canonical Forms for the C-Invariant Tensors

    • Oleg I. Bogoyavlenskij
    Pages 65-76

  7. R-Matrices, Generalized Inverses, and Calogero—Moser—Sutherland Models

    • H. W. Braden
    Pages 77-92

  8. Tricks of the Trade: Relating and Deriving Solvable and Integrable Dynamical Systems

    • Francesco Calogero
    Pages 93-116

  9. Classical and Quantum Partition Functions of the Calogero—Moser—Sutherland Model

    • Ph. Choquard
    Pages 117-125

  10. The Meander Determinant and Its Generalizations

    • P. Di Francesco
    Pages 127-144

  11. Differential Equations for Multivariable Hermite and Laguerre Polynomials

    • J. F. van Diejen
    Pages 145-159

  12. Quantum Currents Realization of the Elliptic Quantum Groups E τ,η(sl2)

    • B. Enriquez
    Pages 161-176

  13. Heisenberg—Ising Spin Chain: Plancherel Decomposition and Chebyshev Polynomials

    • Eugene Gutkin
    Pages 177-192

  14. Ruijsenaars’s Commuting Difference System from Belavin’s Elliptic R-Matrix

    • Koji Hasegawa
    Pages 193-202

  15. Invariants and Eigenvectors for Quantum Heisenberg Chains with Elliptic Exchange

    • V. I. Inozemtsev
    Pages 203-220

  16. The Bispectral Involution as a Linearizing Map

    • Alex Kasman
    Pages 221-229

  17. On Some Quadratic Algebras: Jucys—Murphy and Dunkl Elements

    • Anatol N. Kirillov
    Pages 231-248

  18. Elliptic Solutions to Difference Nonlinear Equations and Nested Bethe Ansatz Equations

    • I. Krichever
    Pages 249-271

  19. Creation Operators for the Calogero—Sutherland Model and Its Relativistic Version

    • Luc Lapointe, Luc Vinet
    Pages 273-297

  20. New Exact Results for Quantum Impurity Problems

    • F. Lesage, H. Saleur, P. Simonetti
    Pages 299-312
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Editors and Affiliations

  • Departamento de Matematicas, Universidad de Chile, Nunoa Santiago, Chile

    Jan Felipe Diejen

  • McGill University, Montreal, Canada

    Luc Vinet

Accessibility Information

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Bibliographic Information

  • Book Title: Calogero—Moser— Sutherland Models

  • Editors: Jan Felipe Diejen, Luc Vinet

  • Series Title: CRM Series in Mathematical Physics

  • DOI: https://doi.org/10.1007/978-1-4612-1206-5

  • Publisher: Springer New York, NY

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media New York 2000

  • Hardcover ISBN: 978-0-387-98968-6Published: 23 March 2000

  • Softcover ISBN: 978-1-4612-7043-0Published: 29 October 2012

  • eBook ISBN: 978-1-4612-1206-5Published: 06 December 2012

  • Series ISSN: 2627-7654

  • Series E-ISSN: 2627-7662

  • Edition Number: 1

  • Number of Pages: XXV, 561

  • Topics: Theoretical, Mathematical and Computational Physics

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