New Symmetries And Integrable Models

Author : Andrzej Frydryszak,Jerzy Lukierski,Ziemowit Popowicz
Publisher : World Scientific
Page : 256 pages
File Size : 49,7 Mb
Release : 2000-08-21
Category : Science
ISBN : 9789814493321

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New Symmetries and Integrable Models by Andrzej Frydryszak,Jerzy Lukierski,Ziemowit Popowicz Pdf

The Max Born Symposia started in 1991 and have been held once or twice a year in different places in Lower Silesia. The scientific topics of the Symposia are closely related with front-line research subjects in theoretical physics. This volume deals with new concepts of symmetries in the theory of fundamental intersections as well as integrable dynamical systems. Contents:Noncommutative Geometry and Quantum GroupsParticles, Strings, Superbranes and Their SUSY ExtensionsIntegrable Models and Related Topics Readership: Theoretical, high-energy and mathematical physicists. Keywords:Symmetries;Fundamental Intersections;Integrable Dynamical Systems;Theoretical Physics;High Energy Physics;Mathematical Physics

Author : Andrzej Frydryszak,Jerzy Lukierski,Z. Popowicz
Publisher : World Scientific
Page : 264 pages
File Size : 41,7 Mb
Release : 2000
Category : Science
ISBN : 9810242700

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Proceedings of XIV Max Born Symposium, New Symmetries and Integrable Models by Andrzej Frydryszak,Jerzy Lukierski,Z. Popowicz Pdf

The Max Born Symposia started in 1991 and have been held once or twice a year in different places in Lower Silesia. The scientific topics of the Symposia are closely related with front-line research subjects in theoretical physics. This volume deals with new concepts of symmetries in the theory of fundamental intersections as well as integrable dynamical systems.

Author : Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy
Publisher : Springer Science & Business Media
Page : 633 pages
File Size : 41,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781447148630

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Symmetries, Integrable Systems and Representations by Kenji Iohara,Sophie Morier-Genoud,Bertrand Rémy Pdf

This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Author : J. Frölich,Gerard 't Hooft,Arthur Jaffe,Gerhard Mack,Pronob K. Mitter,Raymond Stora
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 54,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461534723

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New Symmetry Principles in Quantum Field Theory by J. Frölich,Gerard 't Hooft,Arthur Jaffe,Gerhard Mack,Pronob K. Mitter,Raymond Stora Pdf

Soon after the discovery of quantum mechanics, group theoretical methods were used extensively in order to exploit rotational symmetry and classify atomic spectra. And until recently it was thought that symmetries in quantum mechanics should be groups. But it is not so. There are more general algebras, equipped with suitable structure, which admit a perfectly conventional interpretation as a symmetry of a quantum mechanical system. In any case, a "trivial representation" of the algebra is defined, and a tensor product of representations. But in contrast with groups, this tensor product needs to be neither commutative nor associative. Quantum groups are special cases, in which associativity is preserved. The exploitation of such "Quantum Symmetries" was a central theme at the Ad vanced Study Institute. Introductory lectures were presented to familiarize the participants with the al gebras which can appear as symmetries and with their properties. Some models of local field theories were discussed in detail which have some such symmetries, in par ticular conformal field theories and their perturbations. Lattice models provide many examples of quantum theories with quantum symmetries. They were also covered at the school. Finally, the symmetries which are the cause of the solubility of inte grable models are also quantum symmetries of this kind. Some such models and their nonlocal conserved currents were discussed.

Author : Henrik Aratyn
Publisher : Springer
Page : 400 pages
File Size : 47,8 Mb
Release : 1998-01-28
Category : Mathematics
ISBN : UOM:39015042992225

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Supersymmetry and Integrable Models by Henrik Aratyn Pdf

This book combines supersymmetry modelling in quantum mechanics and integrable models in a unique way. It addresses researchers as well as graduate students. Along with articles that present new technical results, the reader will also find pedagogically written reviews. Recent applications of supersymmetric integrable models are also given.

Author : Mo-lin Ge,Yong-shi Wu
Publisher : World Scientific
Page : 186 pages
File Size : 54,8 Mb
Release : 1995-05-31
Category : Electronic
ISBN : 9789814549752

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New Developments Of Integrable Systems And Long-ranged Interaction Models by Mo-lin Ge,Yong-shi Wu Pdf

This volume covers the recent developments of the exact solvable models, Yangian symmetry, the long-ranged interaction models and high-dimensional integrable systems. The authors are all experts in their fields. The volume provides a systematic introduction to statistical and mathematical physics and contains review papers and other contributions.

Author : Amit K. Roy-Chowdhury
Publisher : CRC Press
Page : 372 pages
File Size : 42,6 Mb
Release : 2021-01-04
Category : Mathematics
ISBN : 9781000153330

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Lie Algebraic Methods in Integrable Systems by Amit K. Roy-Chowdhury Pdf

Over the last thirty years, the subject of nonlinear integrable systems has grown into a full-fledged research topic. In the last decade, Lie algebraic methods have grown in importance to various fields of theoretical research and worked to establish close relations between apparently unrelated systems. The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool. The book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation. It then offers a detailed discussion of prolongation structure and its representation theory, the orbit approach-for both finite and infinite dimension Lie algebra. The author also presents the modern approach to symmetries of integrable systems, including important new ideas in symmetry analysis, such as gauge transformations, and the "soldering" approach. He then moves to Hamiltonian structure, where he presents the Drinfeld-Sokolov approach, the Lie algebraic approach, Kupershmidt's approach, Hamiltonian reductions and the Gelfand Dikii formula. He concludes his treatment of Lie algebraic methods with a discussion of the classical r-matrix, its use, and its relations to double Lie algebra and the KP equation.

Author : Hagen Münkler
Publisher : Springer
Page : 210 pages
File Size : 40,8 Mb
Release : 2018-11-24
Category : Science
ISBN : 9783030036058

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Symmetries of Maldacena-Wilson Loops from Integrable String Theory by Hagen Münkler Pdf

The book discusses hidden symmetries in the Anti-de Sitter/conformal field theory (AdS/CFT) duality. This duality is a modern concept that asserts an exact duality between conformally invariant quantum field theories and string theories in higher dimensional Anti-de Sitter spaces, and in this way provides a completely new tool for the study of strongly coupled quantum field theories. In this setting, the book focuses on the Wilson loop, an important observable in four-dimensional maximally supersymmetric gauge theory. The dual string description using minimal surfaces enables a systematic study of the hidden symmetries of the loop. The book presents major findings, including the discovery of a master symmetry for strings in general symmetric spaces, its relation to the Yangian symmetry algebra and its action on the minimal surfaces appearing in the dual string description of the Wilson loop. Moreover, it clarifies why certain symmetries are not present on the gauge theory side for purely bosonic Wilson loops and, lastly, how the supersymmetrization of the minimal surface problem for type IIB superstrings can be undertaken. As such, it substantially increases our understanding and use of infinite dimensional symmetries occurring in the AdS/CFT correspondence.

Author : Decio Levi,Pavel Winternitz,Ravil I. Yamilov
Publisher : American Mathematical Society, Centre de Recherches Mathématiques
Page : 520 pages
File Size : 55,6 Mb
Release : 2023-01-23
Category : Mathematics
ISBN : 9780821843543

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Continuous Symmetries and Integrability of Discrete Equations by Decio Levi,Pavel Winternitz,Ravil I. Yamilov Pdf

This book on integrable systems and symmetries presents new results on applications of symmetries and integrability techniques to the case of equations defined on the lattice. This relatively new field has many applications, for example, in describing the evolution of crystals and molecular systems defined on lattices, and in finding numerical approximations for differential equations preserving their symmetries. The book contains three chapters and five appendices. The first chapter is an introduction to the general ideas about symmetries, lattices, differential difference and partial difference equations and Lie point symmetries defined on them. Chapter 2 deals with integrable and linearizable systems in two dimensions. The authors start from the prototype of integrable and linearizable partial differential equations, the Korteweg de Vries and the Burgers equations. Then they consider the best known integrable differential difference and partial difference equations. Chapter 3 considers generalized symmetries and conserved densities as integrability criteria. The appendices provide details which may help the readers' understanding of the subjects presented in Chapters 2 and 3. This book is written for PhD students and early researchers, both in theoretical physics and in applied mathematics, who are interested in the study of symmetries and integrability of difference equations.

Author : Boris Kruglikov,Valentin Lychagin,Eldar Straume
Publisher : Springer Science & Business Media
Page : 394 pages
File Size : 40,6 Mb
Release : 2009-07-24
Category : Mathematics
ISBN : 9783642008733

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Differential Equations - Geometry, Symmetries and Integrability by Boris Kruglikov,Valentin Lychagin,Eldar Straume Pdf

The Abel Symposium 2008 focused on the modern theory of differential equations and their applications in geometry, mechanics, and mathematical physics. Following the tradition of Monge, Abel and Lie, the scientific program emphasized the role of algebro-geometric methods, which nowadays permeate all mathematical models in natural and engineering sciences. The ideas of invariance and symmetry are of fundamental importance in the geometric approach to differential equations, with a serious impact coming from the area of integrable systems and field theories. This volume consists of original contributions and broad overview lectures of the participants of the Symposium. The papers in this volume present the modern approach to this classical subject.

Author : Peter A. Clarkson,Frank W. Nijhoff
Publisher : Cambridge University Press
Page : 444 pages
File Size : 48,5 Mb
Release : 1999-02-04
Category : Mathematics
ISBN : 0521596998

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Symmetries and Integrability of Difference Equations by Peter A. Clarkson,Frank W. Nijhoff Pdf

This volume comprises state-of-the-art articles in discrete integrable systems.

Author : Decio Levi
Publisher : American Mathematical Soc.
Page : 402 pages
File Size : 46,9 Mb
Release : 1996
Category : Mathematics
ISBN : 9780821806012

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Symmetries and Integrability of Difference Equations by Decio Levi Pdf

This book is devoted to a topic that has undergone rapid and fruitful development over the last few years: symmetries and integrability of difference equations and q-difference equations and the theory of special functions that occur as solutions of such equations. Techniques that have been traditionally applied to solve linear and nonlinear differential equations are now being successfully adapted and applied to discrete equations. This volume is based on contributions made by leading experts in the field during the workshop on Symmetries and Integrability of Difference Equations held Estérel, Québec, in May 1994. Giving an up-to-date review of the current status of the field, the book treats these specific topics: Lie group and quantum group symmetries of difference and q-difference equations, integrable and nonintegrable discretizations of continuous integrable systems, integrability of difference equations, discrete Painlevé property and singularity confinement, integrable mappings, applications in statistical mechanics and field theories, Yang-Baxter equations, q-special functions and discrete polynomials, and q-difference integrable systems.

Author : Norbert Euler,Da-jun Zhang
Publisher : CRC Press
Page : 510 pages
File Size : 51,5 Mb
Release : 2021-09-07
Category : Mathematics
ISBN : 9781000423266

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Nonlinear Systems and Their Remarkable Mathematical Structures by Norbert Euler,Da-jun Zhang Pdf

The third volume in this sequence of books consists of a collection of contributions that aims to describe the recent progress in nonlinear differential equations and nonlinear dynamical systems (both continuous and discrete). Nonlinear Systems and Their Remarkable Mathematical Structures: Volume 3, Contributions from China just like the first two volumes, consists of contributions by world-leading experts in the subject of nonlinear systems, but in this instance only featuring contributions by leading Chinese scientists who also work in China (in some cases in collaboration with western scientists). Features Clearly illustrate the mathematical theories of nonlinear systems and its progress to both the non-expert and active researchers in this area . Suitable for graduate students in Mathematics, Applied Mathematics and some of the Engineering Sciences. Written in a careful pedagogical manner by those experts who have been involved in the research themselves, and each contribution is reasonably self-contained.

Author : Decio Levi,Raphaël Rebelo,Pavel Winternitz
Publisher : Springer
Page : 435 pages
File Size : 50,9 Mb
Release : 2017-06-30
Category : Science
ISBN : 9783319566665

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Symmetries and Integrability of Difference Equations by Decio Levi,Raphaël Rebelo,Pavel Winternitz Pdf

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations. Difference equations are playing an increasingly important role in the natural sciences. Indeed, many phenomena are inherently discrete and thus naturally described by difference equations. More fundamentally, in subatomic physics, space-time may actually be discrete. Differential equations would then just be approximations of more basic discrete ones. Moreover, when using differential equations to analyze continuous processes, it is often necessary to resort to numerical methods. This always involves a discretization of the differential equations involved, thus replacing them by difference ones. Each of the nine peer-reviewed chapters in this volume serves as a self-contained treatment of a topic, containing introductory material as well as the latest research results and exercises. Each chapter is presented by one or more early career researchers in the specific field of their expertise and, in turn, written for early career researchers. As a survey of the current state of the art, this book will serve as a valuable reference and is particularly well suited as an introduction to the field of symmetries and integrability of difference equations. Therefore, the book will be welcomed by advanced undergraduate and graduate students as well as by more advanced researchers.

Author : Faqir Chand Khanna,Université de Montréal. Centre de recherches mathématiques,Luc Vinet
Publisher : Publications CRM
Page : 228 pages
File Size : 52,7 Mb
Release : 1997
Category : Field theory (Physics)
ISBN : UOM:39015053926930

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Field Theory, Integrable Systems and Symmetries by Faqir Chand Khanna,Université de Montréal. Centre de recherches mathématiques,Luc Vinet Pdf