Calogero-Moser- Sutherland Models
Published on 29. October 2012
Book
Paperback/Softback
XXV, 561 pages
978-1-4612-7043-0 (ISBN)
Description
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.
More details
Series
Edition
Softcover reprint of the original 1st ed. 2000
Language
English
Place of publication
New York
United States
Target group
Professional and scholarly
Research
Illustrations
XXV, 561 p.
Dimensions
Height: 244 mm
Width: 170 mm
Thickness: 32 mm
Weight
1007 gr
ISBN-13
978-1-4612-7043-0 (9781461270430)
DOI
10.1007/978-1-4612-1206-5
Schweitzer Classification
Other editions
Additional editions
Jan F. van Diejen | Luc Vinet
Calogero-Moser- Sutherland Models
E-Book
12/2012
Springer
€53.49
Available for download
Jan F. van Diejen | Luc Vinet
Calogero-Moser- Sutherland Models
Book
04/2000
1st Edition
Springer
€96.00
Article exhausted; check different version
Content
1 Classical Dynamical r-Matrices for Calogero-Moser Systems and Their Generalizations.- 2 Hidden Algebraic Structure of the Calogero-Sutherland Model, Integral Formula for Jack Polynomial and Their Relativistic Analog.- 3 Polynomial Eigenfunctions of the Calogero-Sutherland- Moser Models with Exchange Terms.- 4 The Theory of Lacunas and Quantum Integrable Systems.- 5 Canonical Forms for the C-Invariant Tensors.- 6 R-Matrices, Generalized Inverses, and Calogero-Moser- Sutherland Models.- 7 Tricks of the Trade: Relating and Deriving Solvable and Integratile Dynamical Systems.- 8 Classical and Quantum Partition Functions of the Calogero-Moser-Sutherland Model.- 9 The Meander Determinant and Its Generalizations.- 10 Differential Equations for Multivariable Hermite and Laguerre Polynomials.- 11 Quantum Currents Realization of the Elliptic Quantum Groups E?,?(sl2).- 12 Heisenberg-Ising Spin Chain: Plancherel Decomposition and Chebyshev Polynomials.- 13 Ruijsenaars's Commuting Difference System from Belavin's Elliptic R-Matrix.- 14 Invariants and Eigenvectors for Quantum Heisenberg Chains with Elliptic Exchange.- 15 The Bispectral Involution as a Linearizing Map.- 16 On Some Quadratic Algebras: Jucys-Murphy and Dunkl Elements.- 17 Elliptic Solutions to Difference Nonlinear Equations and Nested Bethe Ansatz Equations.- 18 Creation Operators for the Calogero-Sutherland Model and Its Relativistic Version.- 19 New Exact Results for Quantum Impurity Problems.- 20 Painlevé-Calogero Correspondence.- 21 Yangian Symmetry in WZW Models.- 22 The Quantized Knizhnik-Zamolodchikov Equation in Tensor Products of Irreducible sl2-Modules.- 23 Gauge Fields and Interacting Particles.- 24 Generalizations of Calogero Systems.- 25 Three-Body Generalizations of theSutherland Problem.- 26 On Relativistic Lamé Functions.- 27 Exact Solution for the Ground State of a One-Dimensional Quantum Lattice Gas with Coulomb-Like Interaction.- 28 Differential Operators that Commute with the r?2-type Hamiltonian.- 29 The Distribution of the Largest Eigenvalue in the Gaussian Ensembles: ? = 1, 2, 4.- 30 Two-Body Elliptic Model in Proper Variables: Lie Algebraic Forms and Their Discretizations.- 31 Yangian Gelfand-Zetlin Bases, glN-Jack Polynomials, and Computation of Dynamical Correlation Functions in the Spin Calogero-Sutherland Model.- 32 Thermodynamics of Moser-Calogero Potentials and Seiberg-Witten Exact Solution.- 33 New Integrable Generalizations of the CMS Quantum Problem and Deformations of Root Systems.- 34 The Calogero Model: Integrable Structure and Orthogonal Basis.- 35 The Complex Calogero-Moser and KP Systems.- 36 Oscillator 9j-Symbols, Multidimensional Factorization Method, and Multi variable Krawtchouk Polynomials.