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Friday, July 10, 2020 | History

4 edition of Yang-Baxter equation in integrablesystems found in the catalog.

Yang-Baxter equation in integrablesystems

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  • 13 Currently reading

Published by World Scientific in Singapore, London .
Written in English

    Subjects:
  • Yang-Baxter equation.,
  • Mathematical physics.

  • Edition Notes

    Includes bibliographical references (p. ).

    Statementeditor: Michio Jimbo.
    SeriesAdvanced series in mathematical physics -- vol. 10
    ContributionsJimbo, M.
    Classifications
    LC ClassificationsQC174.52.Y36
    The Physical Object
    Paginationp. cm.
    ID Numbers
    Open LibraryOL22577851M
    ISBN 109810201206, 9810201214

    Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers. Keywords discrete Painlevé equations Orthogonal polynomials Discrete integrable systems Yang-Baxter maps Difference Galois theory multivariable difference equations differential difference equations. The book contains a thorough exposition of such non-perturbative techniques as 1/N-expansion, bosonization (Abelian and non-Abelian), conformal field theory and theory of integrable systems. The book is intended for graduate students, postdoctoral associates and independent researchers working in condensed matter physics.

    After reading several books and articles about integrable systems, and after several years of work in the field, I consider particularly meaningful the following quotation from Frederic Helein's book 'Constant mean curvature surfaces, harmonic maps and integrable systems', Lectures in Mathematics, ETH Zurich, Birkhauser Basel (). Abstract. The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups.

    The Yang–Baxter equation is a consequence of this reducibility and leads to trace identities which provide an infinite set of conserved quantities. All of these ideas are incorporated into the quantum inverse scattering method where the algebraic Bethe ansatz can be used to obtain explicit solutions. The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C.N. Yang and in the work of R.J. Baxter in the field of Statistical Mechanics. At the International Mathematics Congress, Vladimir Drinfeld, Vaughan F. R. Jones, and Edward Witten were.


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Yang-Baxter equation in integrablesystems Download PDF EPUB FB2

Yang-Baxter Equation In Integrable Systems (Advanced Mathematical Physics) Paperback – March 1, by Michio Jimbo (Author) See all Author: Michio Jimbo. The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems (Oxford Lecture Series Yang-Baxter equation in integrablesystems book Mathematics and Its Applications) by Pavel Etingof (Author), Frederic Latour (Author)Cited by: Yang-Baxter equation in integrable systems (Book, ) [] Get this from a library.

Yang-Baxter equation in integrable systems. This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory.

The dynamical Yang-Baxter equation, representation theory, and quantum integrable systems Pavel Etingof, Frederic Latour The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups.

The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems plan to review this book.

Preface 1. Introduction 2. Background material 3. Intertwiners, fusion and exchange operators for Lie algebras 4.

Quantum groups 5. Intertwiners, fusion and exchange operators for UULq (g) 6. Dynamical R-matrices and. We give the basic definitions connected with the Yang-Baxter equation (factorization condition for a multiparticle S-matrix) and formulate the problem of classifying its solutions.

We list the known methods of solution of the Y–B equation, and also various applications of this equation to the theory of completely integrable quantum and.

The constant Yang–Baxter equation, or quantum Yang–Baxter equation, for R is: R12R13R23 = R23R13R12, where Rij is the endomorphism of Cn ⊗ Cn ⊗ Cn acting like R on the two factors i, j and leaving the third factor alone. Thus, R12 = R ⊗ id, R23 = id ⊗ R and. In one dimensional quantum systems, is the scattering matrix and if it satisfies the Yang–Baxter equation then the system is integrable.

The Yang–Baxter equation also shows up when discussing knot theory and the braid groups where corresponds to swapping two strands.

Since one can swap three strands two different ways, the Yang–Baxter equation enforces that both paths are the same.

The Yang-Baxter equation (YBE) is an equation of importance to several areas of research in mathematics and physics. An overview of the YBE can be found in Sections 1 and 2 of [Nic12]. Yang-Baxter equation in integrable systems.

[M Jimbo;] -- "This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S. yang baxter equation in integrable systems by m jimbo world scientific edition in english in physics the yang baxter equation or star triangle relation is a consistency equation which was first introduced in the field of statistical mechanics it depends on the idea that in some scattering situations.

The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups.

Nonlinear Sciences > Exactly Solvable and Integrable Systems. Title: Solving and classifying the solutions of the Yang-Baxter equation through a differential approach. Two-state systems.

Authors: R. Vieira (Submitted on 5 Declast revised 18 Oct (this version, v3)). System Upgrade on Fri, Jun 26th, at 5pm (ET) During this period, our website will be offline for less than an hour but the E-commerce and registration of new. Kulish P.P. () Yang-Baxter equation and reflection equations in integrable models.

In: Grosse H., Pittner L. (eds) Low-Dimensional Models in Statistical Physics and Quantum Field Theory. Lecture Notes in Physics, vol The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems This nice small book, based on a course given at MIT inis devoted to connections of quantum dynamical Yang-Baxter equations with certain integrable systems and representations of semisimple Lie algebras and of quantum groups.

This paper contains a systematic and elementary introduction to a new area of the theory of quantum groups -- the theory of the classical and quantum dynamical Yang-Baxter equations.

It arose from a minicourse given by the first author at MIT in the Spring ofwhen the second author extended and improved his lecture notes of this minicourse. The quantum dynamical Yang-Baxter equation. This volume will be the first reference book devoted specially to the Yang-Baxter equation.

The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory.

The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter. Quantum integrable models associated with nondegenerate solutions of classical Yang–Baxter equations related to the simple Lie algebras are investigated. These models are diagonalized for rational and trigonometric solutions in the cases of sl (N)/gl (N)/, o (N) and sp (N) algebras.

In a recent paper, the so-called Yang–Baxter-like matrix equation () A X A = X A X was solved completely, where A = p q T is a given n × n complex matrix of rank one with two nonzero n-dimensional vectors p and q.

Eq.This book arose from lectures given by the author in an attempt to reformulate the results of the rapidly developing research and make the material more accessible. It explains the presentation of the Yang-Baxter equation from statistical models, and expound systematically the meaning and methods of solving for this equation.Jimbo, M.Yang-Baxter equation in integrable systems / editor, Michio Jimbo World Scientific Singapore Wikipedia Citation Please see Wikipedia's template documentation for further citation fields that may be required.