Michio Jimbo's Books

Local Operators in Integrable Models I

By: Michio Jimbo,Tetsuji Miwa,Fedor Smirnov

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Local Operators in Integrable Models I

By: Michio Jimbo,Tetsuji Miwa,Fedor Smirnov

Integrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published monograph on this subject. It treats integrable lattice models, notably the six-vertex model and the XXZ Heisenberg spin chain. A pair of fermions is introduced and used to create a basis of the space of local operators, leading to the result that all correlation functions at finite distances are expressible in terms of two transcendental functions with rational coefficients. Step-by-step explanations are given for all materials necessary for this construction, ranging from algebraic Bethe ansatz, representations of quantum groups, and the Bazhanov-Lukyanov-Zamolodchikov construction in conformal field theory to Riemann surfaces and their Jacobians. Several examples and applications are given along with numerical results. Going through the book, readers will find themselves at the forefront of this rapidly developing research field.

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Page Count

192

Publisher

American Mathematical Soc.

Published Date

ISBN 10

1470465523

ISBN 13

9781470465520

Yang-baxter Equation In Integrable Systems

By: Michio Jimbo

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Yang-baxter Equation In Integrable Systems

By: Michio 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 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./a

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Page Count

727

Publisher

World Scientific

Published Date

ISBN 10

9814507067

ISBN 13

9789814507066

Algebraic Analysis of Solvable Lattice Models

By: Michio Jimbo,Tetsuji Miwa

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Algebraic Analysis of Solvable Lattice Models

By: Michio Jimbo,Tetsuji Miwa

Based 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.

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Page Count

180

Publisher

American Mathematical Soc.

Published Date

ISBN 10

0821803204

ISBN 13

9780821803202

Strings, Conformal Fields, and Topology

An Introduction

By: Michio Kaku

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Strings, Conformal Fields, and Topology

An Introduction

By: Michio Kaku

Following on the foundations laid in his earlier book "Introduction to Superstrings", Professor Kaku discusses such topics as the classification of conformal string theories, the non-polynomial closed string field theory, matrix models, and topological field theory. The presentation of the material is self-contained, and several chapters review material expounded in the earlier book. This book provides students with an understanding of the main areas of current progress in string theory, placing the reader at the forefront of current research.

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Page Count

544

Publisher

Springer Science & Business Media

Published Date

ISBN 10

1468403974

ISBN 13

9781468403978

New Trends in Quantum Integrable Systems

Proceedings of the Infinite Analysis 09 : Kyoto, Japan 27-31 July 2009

By: Boris Feigin,Michio Jimbo,Masato Okado

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New Trends in Quantum Integrable Systems

Proceedings of the Infinite Analysis 09 : Kyoto, Japan 27-31 July 2009

By: Boris Feigin,Michio Jimbo,Masato Okado

The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project "Method of Algebraic Analysis in Integrable Systems" in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years. Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics. Through these topics, the reader is exposed to the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

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Page Count

517

Publisher

World Scientific

Published Date

ISBN 10

9814324361

ISBN 13

9789814324366

Yang-baxter Equation In Integrable Systems

By: Michio Jimbo

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Yang-baxter Equation In Integrable Systems

By: Michio Jimbo

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Page Count

727

Publisher

World Scientific

Published Date

ISBN 10

9814507067

ISBN 13

9789814507066

New Trends in Quantum Integrable Systems

Proceedings of the Infinite Analysis 09 : Kyoto, Japan 27-31 July 2009

By: Boris Feigin,Michio Jimbo,Masato Okado

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New Trends in Quantum Integrable Systems

Proceedings of the Infinite Analysis 09 : Kyoto, Japan 27-31 July 2009

By: Boris Feigin,Michio Jimbo,Masato Okado

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Solve jigsaw puzzle

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Page Count

517

Publisher

World Scientific

Published Date

ISBN 10

9814324361

ISBN 13

9789814324366

Book's by Michio Jimbo

Local Operators in Integrable Models I

Local Operators in Integrable Models I

Yang-baxter Equation In Integrable Systems

Yang-baxter Equation In Integrable Systems

Algebraic Analysis of Solvable Lattice Models

Algebraic Analysis of Solvable Lattice Models

Strings, Conformal Fields, and Topology

Strings, Conformal Fields, and Topology

New Trends in Quantum Integrable Systems

New Trends in Quantum Integrable Systems

Yang-baxter Equation In Integrable Systems

Yang-baxter Equation In Integrable Systems

New Trends in Quantum Integrable Systems

New Trends in Quantum Integrable Systems

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