Integrability Quantization And Geometry I Integrable Systems

Author : Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Publisher : American Mathematical Soc.
Page : 516 pages
File Size : 44,7 Mb
Release : 2021-04-12
Category : Education
ISBN : 9781470455910

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Integrability, Quantization, and Geometry: I. Integrable Systems by Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman Pdf

This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

Author : Sergeĭ Petrovich Novikov,I. M. Krichever,Oleg Ogievetsky,S. Shlosman
Publisher : Unknown
Page : 542 pages
File Size : 46,9 Mb
Release : 2021
Category : Electronic books
ISBN : 1470464349

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Integrability, Quantization, and Geometry by Sergeĭ Petrovich Novikov,I. M. Krichever,Oleg Ogievetsky,S. Shlosman Pdf

This book is a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.The contributions to this collection of papers are split into two parts: ""Integrable Systems"" and ""Quantum Theories and Algebraic Geometry"", reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, i.

Author : Pol Vanhaecke
Publisher : Springer
Page : 226 pages
File Size : 55,7 Mb
Release : 2013-11-11
Category : Mathematics
ISBN : 9783662215357

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Integrable Systems in the realm of Algebraic Geometry by Pol Vanhaecke Pdf

Integrable systems are related to algebraic geometry in many different ways. This book deals with some aspects of this relation, the main focus being on the algebraic geometry of the level manifolds of integrable systems and the construction of integrable systems, starting from algebraic geometric data. For a rigorous account of these matters, integrable systems are defined on affine algebraic varieties rather than on smooth manifolds. The exposition is self-contained and is accessible at the graduate level; in particular, prior knowledge of integrable systems is not assumed.

Author : Lionel Mason,Yavuz Nutku
Publisher : Cambridge University Press
Page : 170 pages
File Size : 54,7 Mb
Release : 2003-11-20
Category : Mathematics
ISBN : 0521529999

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Geometry and Integrability by Lionel Mason,Yavuz Nutku Pdf

Most integrable systems owe their origin to problems in geometry and they are best understood in a geometrical context. This is especially true today when the heroic days of KdV-type integrability are over. Problems that can be solved using the inverse scattering transformation have reached the point of diminishing returns. Two major techniques have emerged for dealing with multi-dimensional integrable systems: twistor theory and the d-bar method, both of which form the subject of this book. It is intended to be an introduction, though by no means an elementary one, to current research on integrable systems in the framework of differential geometry and algebraic geometry. This book arose from a seminar, held at the Feza Gursey Institute, to introduce advanced graduate students to this area of research. The articles are all written by leading researchers and are designed to introduce the reader to contemporary research topics.

Author : Chuu-lian Terng
Publisher : American Mathematical Soc.
Page : 270 pages
File Size : 40,9 Mb
Release : 2006
Category : Geometry
ISBN : 9780821840481

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Integrable Systems, Geometry, and Topology by Chuu-lian Terng Pdf

The articles in this volume are based on lectures from a program on integrable systems and differential geometry held at Taiwan's National Center for Theoretical Sciences. As is well-known, for many soliton equations, the solutions have interpretations as differential geometric objects, and thereby techniques of soliton equations have been successfully applied to the study of geometric problems. The article by Burstall gives a beautiful exposition on isothermic surfaces and theirrelations to integrable systems, and the two articles by Guest give an introduction to quantum cohomology, carry out explicit computations of the quantum cohomology of flag manifolds and Hirzebruch surfaces, and give a survey of Givental's quantum differential equations. The article by Heintze, Liu,and Olmos is on the theory of isoparametric submanifolds in an arbitrary Riemannian manifold, which is related to the n-wave equation when the ambient manifold is Euclidean. Mukai-Hidano and Ohnita present a survey on the moduli space of Yang-Mills-Higgs equations on Riemann surfaces. The article by Terng and Uhlenbeck explains the gauge equivalence of the matrix non-linear Schrödinger equation, the Schrödinger flow on Grassmanian, and the Heisenberg Feromagnetic model. The bookprovides an introduction to integrable systems and their relation to differential geometry. It is suitable for advanced graduate students and research mathematicians. Information for our distributors: Titles in this series are copublished with International Press, Cambridge, MA.

Author : J. Hietarinta,N. Joshi,F. W. Nijhoff
Publisher : Cambridge University Press
Page : 461 pages
File Size : 51,8 Mb
Release : 2016-09
Category : Mathematics
ISBN : 9781107042728

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Discrete Systems and Integrability by J. Hietarinta,N. Joshi,F. W. Nijhoff Pdf

A first introduction to the theory of discrete integrable systems at a level suitable for students and non-experts.

Author : Ron Donagi,Tony Shaska
Publisher : Cambridge University Press
Page : 421 pages
File Size : 55,7 Mb
Release : 2020-04-02
Category : Mathematics
ISBN : 9781108715744

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Integrable Systems and Algebraic Geometry by Ron Donagi,Tony Shaska Pdf

A collection of articles discussing integrable systems and algebraic geometry from leading researchers in the field.

Author : R. Carroll
Publisher : Elsevier
Page : 420 pages
File Size : 55,7 Mb
Release : 2000-11-09
Category : Science
ISBN : 0080540082

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Quantum Theory, Deformation and Integrability by R. Carroll Pdf

About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory.

Author : Gleb Arutyunov
Publisher : Springer
Page : 414 pages
File Size : 42,8 Mb
Release : 2019-07-23
Category : Science
ISBN : 9783030241988

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Elements of Classical and Quantum Integrable Systems by Gleb Arutyunov Pdf

Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

Author : Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman
Publisher : American Mathematical Soc.
Page : 480 pages
File Size : 50,8 Mb
Release : 2021-04-12
Category : Education
ISBN : 9781470455927

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Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry by Sergey Novikov,Igor Krichever,Oleg Ogievetsky,Senya Shlosman Pdf

This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.

Author : A.K. Prykarpatsky,I.V. Mykytiuk
Publisher : Springer Science & Business Media
Page : 555 pages
File Size : 41,6 Mb
Release : 2013-04-09
Category : Science
ISBN : 9789401149945

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Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds by A.K. Prykarpatsky,I.V. Mykytiuk Pdf

In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).

Author : Pierre Dazord,Alan Weinstein
Publisher : Springer Science & Business Media
Page : 318 pages
File Size : 41,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461397199

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Symplectic Geometry, Groupoids, and Integrable Systems by Pierre Dazord,Alan Weinstein Pdf

The papers, some of which are in English, the rest in French, in this volume are based on lectures given during the meeting of the Seminare Sud Rhodanien de Geometrie (SSRG) organized at the Mathematical Sciences Research Institute in 1989. The SSRG was established in 1982 by geometers and mathematical physicists with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. Among the subjects discussed at the meeting, a special role was given to the theory of symplectic groupoids, the subject of fruitful collaboration involving geometers from Berkeley, Lyon, and Montpellier.

Author : Ivailo M. Mladenov,Gregory L. Naber
Publisher : Unknown
Page : 308 pages
File Size : 50,7 Mb
Release : 2000
Category : Biomathematics
ISBN : UOM:39015054175313

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Geometry, Integrability and Quantization by Ivailo M. Mladenov,Gregory L. Naber Pdf

Author : Lionel J. Mason,Nicholas Michael John Woodhouse
Publisher : Oxford University Press
Page : 384 pages
File Size : 45,6 Mb
Release : 1996
Category : Language Arts & Disciplines
ISBN : 0198534981

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Integrability, Self-duality, and Twistor Theory by Lionel J. Mason,Nicholas Michael John Woodhouse Pdf

Many of the familiar integrable systems of equations are symmetry reductions of self-duality equations on a metric or on a Yang-Mills connection. For example, the Korteweg-de Vries and non-linear Schrodinger equations are reductions of the self-dual Yang-Mills equation. This book explores in detail the connections between self-duality and integrability, and also the application of twistor techniques to integrable systems. It supports two central theories: that the symmetries of self-duality equations provide a natural classification scheme for integrable systems; and that twistor theory provides a uniform geometric framework for the study of Backlund transformations, the inverse scattering method, and other such general constructions of integrability theory. The book will be useful to researchers and graduate students in mathematical physics.

Author : Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita
Publisher : American Mathematical Soc.
Page : 348 pages
File Size : 53,9 Mb
Release : 2002
Category : Mathematics
ISBN : 0821856456

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Integrable Systems, Topology, and Physics by Martin A. Guest,Reiko Miyaoka,Yoshihiro Ohnita Pdf

A major international conference was held at the University of Tokyo in July 2000. It brought together scientists in all of the areas influenced by integrable systems. This book is the second of three collections of expository and research articles. This volume focuses on topology and physics.