Download or read book Yang-Baxter Equation in Integrable Systems written by Michio Jimbo and published by World Scientific. This book was released on 1990-03-01 with total page 728 pages. Available in PDF, EPUB and Kindle. Book excerpt: ' 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 equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions. Contents:Some Exact Results for the Many-Body Problem in One Dimension with Repulsive Delta-Function Interaction (C N Yang)S matrix for the One Dimensional N-Body Problem with Repulsive or Attractive δ-Function Interaction (C N Yang)Partition Function of the Eight-Vertex Lattice Model (R J Baxter)Solutions of the Classical Yang-Baxter Equation and Simple Lie Algebras (A A Belavin & V G Drinfel'd)Some Algebraic Structures Connected with the Yang-Baxter Equation (E K Sklyanin)Quantization of Lie Groups and Lie Algebras (L D Faddeev, N Yu Reshetikhin & L A Takhtajan)Families of Commuting Transfer Matrices in q-State Vertex Models in Non-Linear Integrable Systems — Classical Theory and Quantum Theory (J H H Perk & C L Schultz)Self-Dual Solutions of the Star-Triangle Relations in ZN Models (V A Fateev & A B Zamolodchikov)Solvable Lattice Models Related to the Vector Representation of Classical Simple Lie Algebras (M Jimbo, T Miwa & M Okado)Exactly Solvable SOS Models. II: Proof of the Star-Triangle and Combinatorial Identities (E Date et al.)New Solutions of the Star-Triangle Relations for the Chiral Potts Model (R J Baxter, J H H Perk & H Au-Yang)and other papers Readership: Physicists and mathematicians. Keywords:Yang-Baxter Equation;Star-Triangle Relation;Tetrahedron Equation;R Matrix;Classical R Matrix;Solvable Lattice Model;Factorized Scattering;Quantum Inverse Method;Quantum Groups;Lie Algebra“The collection serves a dual purpose: it provides the physicist or mathematician who works in a different field with an overview of the subject; furthermore, it provides those who work in the subject with a compendium of basic references put conveniently together in one volume.”Mathematical Reveiws “Thus the book gives a good survey of results in one of the hottest points of mathematical physics from the first hands.”Mathematics Abstracts “The second volume is such an excellent, representative collection of articles on the very rich field centered around the Yang-Baxter equation that is should have its place on the shelves of every good library. It is also warmly recommended for people wishing to join this active research area as well as for those who just want to learn the main developments.”Acta Sci. Math. (Szeged) '