Lie Algebras and Exactly Solvable Lattice Models
Author: Martin O'Loughlin
Publisher:
Published: 1988
Total Pages: 16
ISBN-13: 9780868399409
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Author: Martin O'Loughlin
Publisher:
Published: 1988
Total Pages: 16
ISBN-13: 9780868399409
DOWNLOAD EBOOKAuthor: Michio Jimbo
Publisher: American Mathematical Soc.
Published: 1995
Total Pages: 180
ISBN-13: 0821803204
DOWNLOAD EBOOKBased on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin 1/2 XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the XXX model is briefly discussed, and the book closes with a discussion of other types of models and related works.
Author: M Jimbo
Publisher: Elsevier
Published: 2012-12-02
Total Pages: 439
ISBN-13: 0323150357
DOWNLOAD EBOOKAdvanced Studies in Pure Mathematics, 16: Conformal Field Theory and Solvable Lattice Models contains nine papers based on the symposium "Conformal field theory and solvable lattice models" held at RIMS, Kyoto, May 1986. These papers cover the following active areas in mathematical physics: conformal field theory, solvable lattice models, affine and Virasoro algebra, and KP equations. The volume begins with an analysis of 1 and 2 point correlation functions of the Gibbs measure of random matrices. This is followed by separate chapters on solvable solid-on-solid (SOS) models; lectures on conformal field theory; the construction of Fermion variables for the 3D Ising Model; and vertex operator construction of null fields (singular vertex operators) based on the oscillator representation of conformal and superconformal algebras with central charge extention. Subsequent chapters deal with Hecke algebra representations of braid groups and classical Yang-Baxter equations; the relationship between the conformal field theories and the soliton equations (KdV, MKdV and Sine-Gordon, etc.) at both quantum and classical levels; and a supersymmetric extension of the Kadomtsev-Petviashvili hierarchy.
Author: Seok-Jin Kang
Publisher: American Mathematical Soc.
Published: 1996
Total Pages: 242
ISBN-13: 0821805126
DOWNLOAD EBOOKOver the past 30 years, exciting developments in diverse areas of the theory of Lie algebras and their representations have been observed. The symposium covered topics such as Lie algebras and combinatorics, crystal bases for quantum groups, quantum groups and solvable lattice models, and modular and infinite-dimensional Lie algebras. In this volume, readers will find several excellent expository articles and research papers containing many significant new results in this area.
Author: Michael Baake
Publisher: World Scientific
Published: 1995-01-23
Total Pages: 311
ISBN-13: 9814501042
DOWNLOAD EBOOKThis volume consists of a collection of recent research articles dedicated to Vladimir Rittenberg on the occasion of his 60th birthday. Various aspects of solvable models in different areas of theoretical and mathematical physics are covered. Particular topics include diffusion, self-organized criticality, classical and quantum spin chains, two-dimensional lattice models, quantum algebras, and conformal field theory. The list of contributing authors contains altogether 34 names, including among others, Baxter, Cardy, Itzykson, Martin, McCoy, Nahm, Pearce and de Vega.
Author: S. L. Lukyanov
Publisher: CRC Press
Published: 1991
Total Pages: 132
ISBN-13: 9783718650477
DOWNLOAD EBOOKAuthor: Michio Jimbo
Publisher: World Scientific
Published: 1990
Total Pages: 740
ISBN-13: 9789810201203
DOWNLOAD EBOOKThis 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.
Author: Fa Yueh Wu
Publisher: World Scientific
Published: 2009
Total Pages: 661
ISBN-13: 9812813896
DOWNLOAD EBOOKThis unique volume provides a comprehensive overview of exactly solved models in statistical mechanics by looking at the scientific achievements of F Y Wu in this and related fields, which span four decades of his career. The book is organized into topics ranging from lattice models in condensed matter physics to graph theory in mathematics, and includes the author's pioneering contributions. Through insightful commentaries, the author presents an overview of each of the topics and an insider's look at how crucial developments emerged. With the inclusion of important pedagogical review articles by the author, Exactly Solved Models is an indispensable learning tool for graduate students, and an essential reference and source book for researchers in physics and mathematics as well as historians of science.
Author: S. Pakuliak
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 334
ISBN-13: 9401006709
DOWNLOAD EBOOKIntegrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.
Author: Alan L. Carey
Publisher: Cambridge University Press
Published: 1998
Total Pages: 308
ISBN-13: 9780521624909
DOWNLOAD EBOOKGraduate lectures on the interface between mathematics and physics.