Yang Baxter Deformation Of 2d Non Linear Sigma Models

Author : Kentaroh Yoshida
Publisher : Springer Nature
Page : 79 pages
File Size : 40,6 Mb
Release : 2021-06-03
Category : Science
ISBN : 9789811617034

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Yang–Baxter Deformation of 2D Non-Linear Sigma Models by Kentaroh Yoshida Pdf

In mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, non-perturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold–Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or action-angle variables. Recently, a new, systematic method to perform integrable deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang–Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang–Baxter deformation to string theory are also described briefly.

Author : Kentaroh Yoshida
Publisher : Unknown
Page : 0 pages
File Size : 42,5 Mb
Release : 2021
Category : Electronic
ISBN : 981161704X

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Yang-Baxter Deformation of 2D Non-Linear Sigma Models by Kentaroh Yoshida Pdf

In mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, non-perturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold-Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or action-angle variables. Recently, a new, systematic method to perform integrable deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang-Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang-Baxter deformation to string theory are also described briefly. .

Author : Vladimir Dobrev
Publisher : Springer Nature
Page : 552 pages
File Size : 48,7 Mb
Release : 2020-10-15
Category : Science
ISBN : 9789811577758

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Lie Theory and Its Applications in Physics by Vladimir Dobrev Pdf

This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Author : Satoshi Iso,Hiroshi Itoyama,Kazunobu Maruyoshi,Takahiro Nishinaka,Takeshi Oota,Kazuhiro Sakai,Asato Tsuchiya,Reiji Yoshioka
Publisher : World Scientific
Page : 175 pages
File Size : 48,9 Mb
Release : 2022-06-06
Category : Science
ISBN : 9789811261640

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Proceedings Of The East Asia Joint Symposium On Fields And Strings 2021 by Satoshi Iso,Hiroshi Itoyama,Kazunobu Maruyoshi,Takahiro Nishinaka,Takeshi Oota,Kazuhiro Sakai,Asato Tsuchiya,Reiji Yoshioka Pdf

This volume contains the proceedings of the East Asia Joint Symposium on Fields and Strings 2021, held at the Media Center of Osaka City University on November 22-27, 2021. About 160 physicists from all over East Asia attended physically or joined online this symposium and more than 50 researchers presented their results in the invited lectures, the short talks or the poster session. Quantum field theory and string theory in the context of several exciting developments were discussed, which include frontiers of supersymmetric gauge theory, anomalies and higher form symmetries, and several issues on quantum gravity and black holes.

Author : Michio Jimbo
Publisher : World Scientific
Page : 740 pages
File Size : 49,5 Mb
Release : 1990
Category : Science
ISBN : 9810201214

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Yang-Baxter Equation in Integrable Systems by Michio Jimbo Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 640 pages
File Size : 46,9 Mb
Release : 1993
Category : Particles (Nuclear physics)
ISBN : PSU:000052636295

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High Energy Physics Index by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 916 pages
File Size : 51,8 Mb
Release : 1994
Category : Physics
ISBN : UOM:39015027832958

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Physics Briefs by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 952 pages
File Size : 46,7 Mb
Release : 1985
Category : Nuclear energy
ISBN : UOM:39015048698669

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INIS Atomindex by Anonim Pdf

Author : Anonim
Publisher : Unknown
Page : 1432 pages
File Size : 41,8 Mb
Release : 2003
Category : Mathematics
ISBN : UOM:39015058562326

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Mathematical Reviews by Anonim Pdf

Author : Decio Levi,Luc Vinet,Pavel Winternitz
Publisher : American Mathematical Soc.
Page : 404 pages
File Size : 53,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821870505

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Symmetries and Integrability of Difference Equations by Decio Levi,Luc Vinet,Pavel Winternitz Pdf

Author : Jean-Pierre Françoise,Gregory L. Naber,Sheung Tsun Tsou
Publisher : Academic Press
Page : 608 pages
File Size : 41,6 Mb
Release : 2006
Category : Mathematics
ISBN : UCSC:32106018859881

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Encyclopedia of Mathematical Physics by Jean-Pierre Françoise,Gregory L. Naber,Sheung Tsun Tsou Pdf

The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: Jean-Pierre Françoise, Université Pierre et Marie Curie, Paris, France Gregory L. Naber, Drexel University, Philadelphia, PA, USA Tsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006) - featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy.

Author : Vyjayanthi Chari,Andrew N. Pressley
Publisher : Cambridge University Press
Page : 672 pages
File Size : 41,9 Mb
Release : 1995-07-27
Category : Mathematics
ISBN : 0521558840

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A Guide to Quantum Groups by Vyjayanthi Chari,Andrew N. Pressley Pdf

Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.

Author : V. E. Korepin,Vladimir E. Korepin,N. M. Bogoliubov,A. G. Izergin
Publisher : Cambridge University Press
Page : 582 pages
File Size : 51,7 Mb
Release : 1997-03-06
Category : Mathematics
ISBN : 0521586461

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Quantum Inverse Scattering Method and Correlation Functions by V. E. Korepin,Vladimir E. Korepin,N. M. Bogoliubov,A. G. Izergin Pdf

The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.

Author : L. Bonora,Giuseppe Mussardo,A. Schwimmer,L. Girardello,M. Martellini
Publisher : Springer Science & Business Media
Page : 330 pages
File Size : 49,7 Mb
Release : 2013-11-11
Category : Science
ISBN : 9781489915160

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Integrable Quantum Field Theories by L. Bonora,Giuseppe Mussardo,A. Schwimmer,L. Girardello,M. Martellini Pdf

Proceedings of a NATO ARW held in Como, Italy, September 14-19, 1992

Author : Olivier Babelon,Denis Bernard,Michel Talon
Publisher : Cambridge University Press
Page : 622 pages
File Size : 43,7 Mb
Release : 2003-04-17
Category : Mathematics
ISBN : 052182267X

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Introduction to Classical Integrable Systems by Olivier Babelon,Denis Bernard,Michel Talon Pdf

This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.