Calogero—Moser— Sutherland Models - Brossura

Brossura

ISBN 10: 146127043X ISBN 13: 9781461270430

Casa editrice: Springer, 2012

Riassunto

The chapters in this book treat one of the few classes of problems involving more than one particle for which the equations of quantum mechanics are exactly solvable. These so-called Calogero-Moser- Sutherland models now play a role in research areas in theoretical physics (from soliton theory to statistical mechanics) and mathematics (from representation theory to complex geometry).

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Contenuti

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 the Sutherland 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.

Dettagli dell'edizione

• Editore: Springer
• Data di pubblicazione: 2012
• Lingua: Inglese
• ISBN 10: 146127043X
• ISBN 13: 9781461270430
• Rilegatura: Copertina flessibile
• Numero di pagine: 592
• Redattore: Diejen Jan F. Van, Vinet Luc
• Contatto del produttore: Springer Nature Customer Service Center GmbH; ProductSafety@springernature.com; ; Europaplatz 3; Heidelberg; 69115; Germania