Integrable Systems in Quantum  Field Theory and Statistical Mechanics - 1st Edition - ISBN: 9780123853424, 9781483295251

Integrable Systems in Quantum Field Theory and Statistical Mechanics

1st Edition

Editors: M. Jimbo T. Miwa A. Tsuchiya
eBook ISBN: 9781483295251
Imprint: Academic Press
Published Date: 28th January 1990
Page Count: 682
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Description

Advanced Studies in Pure Mathematics, Volume 19: Integrable Systems in Quantum Field Theory and Statistical Mechanics provides information pertinent to the advances in the study of pure mathematics. This book covers a variety of topics, including statistical mechanics, eigenvalue spectrum, conformal field theory, quantum groups and integrable models, integrable field theory, and conformal invariant models. Organized into 17 chapters, this volume begins with an overview of the eigenvalues of the three-state superintegrable chiral Potts model of the associated spin chain by use of a functional equation. This text then illustrates the importance of the star-triangle equation with a few results for the two-dimensional Ising model. Other chapters consider the conformal field theories on manifolds with a boundary, and the constraints placed by modular invariance on their partition functions. This book discusses as well the topological invariants for knots and links. The final chapter deals with equations of motion for two-dimensional quantum field theory. This book is a valuable resource for mathematicians.

Table of Contents


Eigenvalue Spectrum of the Superintegrable Chiral Potts Model

Star-Triangle Relation

Solving Models in Statistical Mechanics

KdV-Type Equations and W-Algebras

Boundary Conditions in Conformal Field Theory

Paths, Maya Diagrams and Representations of sl(r, C)

Knot Theory based on Statistical Models at Criticality

From the Harmonic Oscillator to the A-D-E Classification of Conformal Models

Formal Groups and Conformal Field Theory over Z

A New Family of Solvable Lattice Models Associated with An(1)

Solvable Lattice Models and Algebras of Face Operators

D-Modules and Nonlinear Systems

Quantum Groups and Integrable Models

Conformal Field Theory on Universal Family of Stable Curves with Gauge Symmetries

Yang-Baxter Algebras, Conformal Invariant Models and Quantum Groups

Integrable Field Theory from Conformal Field Theory

Errata to Vertex Operators in Conformal Field Theory on P1 and Monodromy Representations of Braid Group in Advanced Studies in Pure Mathematics 16, 1988

Details

No. of pages:
682
Language:
English
Copyright:
© Academic Press 1989
Published:
Imprint:
Academic Press
eBook ISBN:
9781483295251

About the Editor

M. Jimbo

Affiliations and Expertise

Kyoto University

T. Miwa

Affiliations and Expertise

Kyoto University

A. Tsuchiya

Affiliations and Expertise

Nagoya University