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Wednesday, November 25, 2020 | History

5 edition of Integrable systems and quantum groups found in the catalog.

Integrable systems and quantum groups

lectures given at the 1st session of the Centro internazionale matematico estivo (C.I.M.E.) held in Montecatini Terme, Italy, June 14-22, 1995

by

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  • 1 Currently reading

Published by Springer in New York .
Written in English

    Subjects:
  • Quantum groups.,
  • Geometry, Algebraic.,
  • Mathematical physics.

  • Edition Notes

    Includes bibliographical references.

    StatementR. Donagi ... [et al.] ; editors, M. Francaviglia, S. Greco.
    SeriesLecture notes in mathematics -- 1620., Lecture notes in mathematics (Springer-Verlag) -- 1620.
    ContributionsDonagi, Ron., Francaviglia, M., Greco, Silvio., Centro internazionale matematico estivo.
    Classifications
    LC ClassificationsQC20.7.G76 I56 1995
    The Physical Object
    Paginationvi, 488 p. :
    Number of Pages488
    ID Numbers
    Open LibraryOL18082162M
    ISBN 103540605428
    LC Control Number95045943


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Integrable systems and quantum groups Download PDF EPUB FB2

The aim of this CIME Session was to review the state of the art in the recent development of the theory of integrable systems and their relations with quantum groups. The purpose was to gather geometers and mathematical physicists to allow a broader and more complete view of these attractive and rapidly developing fields.

: Integrable Systems and Quantum Groups: Lectures given at the 1st Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Montecatini(Lecture Notes in Mathematics) (): Ron Donagi, Boris Dubrovin, Edward Frenkel, Emma Previato, Mauro Francaviglia, Silvio Greco: Books.

Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the : Paperback.

Among them, we should mention the new mathematical structures related to integrability and quantum field theories, such as quantum groups, conformal field theories, integrable statistical models, and topological quantum field theories, that are discussed at length by some of the leading experts on the areas in several of the lectures contained in the book.

About this book The aim of this CIME Session was to review the state of the art in the recent development of the theory of integrable systems and their relations with quantum groups. The purpose was to gather geometers and mathematical physicists to allow a broader and more complete view of these attractive and rapidly developing fields.

First of all, while classical integrable systems are related to ordinary Lie groups, quantum systems quite often (though not always,cf. the discussion in section 3) require the full machinery of Quantum Groups. The background took several years to prepare (Drinfeld (a)).

Second. The XXVIIth International Conference on Integrable Systems is one of a series of annual meetings held at the Czech Technical University since and is devoted to problems of mathematical physics related to the theory of integrable systems, quantum groups and quantum symmetries.

It is essential reading to those working in the fields of Quantum Groups, and Integrable Systems. Contents: Topics from Representations of Uq(g) — An Introductory Guide to Physicists (M Jimbo) Quantum Inverse Scattering Method. Selected Topics (E K Sklyanin) Quantum Algebras, q-deformed Oscillators and Related Topics (P P Kulish).

This textbook is designed to give graduate students an understanding of integrable systems via the study of Riemann surfaces, loop groups, and twistors. The book has its origins in a series of lecture courses given by the authors, all of whom are internationally known mathematicians and renowned expositors.

It is written in an accessible and informal style, and fills a gap in the existing. Integrable systems and quantum groups Article (PDF Available)   in   Brazilian Journal of Physics 30(2)   June   with  13 Reads  How we measure 'reads' A 'read' is counted each time someone.

The study of quantum groups, or quantum algebras [7, 8] is crucial to the understanding of integrable systems as well Integrable systems and quantum groups book the development of new integrable models.

It also grew as an independent area in mathematical physics showing interesting connections with other mathematical subjects such as knot theory and non-commutative geometry. Now, as for classification and identification of (new) integrable systems of PDEs, at least in two independent variables, it turns out that the (infinitesimal higher) symmetries play an important role here.

A recent collective monograph Integrability, edited by A.V. Mikhailov and published by Springer in.

Advanced Studies in Pure Mathematics, Volume 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.

The quantum groups discussed in this book are the quantized enveloping algebras introduced by Drinfeld and Jimbo inor variations thereof. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties.

Advanced Studies in Pure Mathematics, Volume 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 Book Edition: 1.

In this thesis we address several questions involving quantum groups, quantum cluster algebras, and integrable systems, and provide some novel examples of the very useful inter-play between these subjects. In the Chapter 2, we introduce the classical re ection equation (CRE), and give a construction of integrable Hamiltonian systems on G=K.

quantum D-module directly, we take an indirect approach. This has the advan-tage that our point of view can accommodate other integrable systems, which may only partially resemble quantum cohomology. To put this in context, in Chapters we review some of the famous (infinite-dimensional) integrable systems, concentrating on the KdV equation.

tum groups, and representation theory. There are also natural origins via quantum integrable systems and the quantization of classical integrable systems.

The latter is often expressed via a q-hierarchy picture akin to the standard Hirota–Lax–Sato formulation and this has many canonical aspects. adshelp[at] The ADS is operated by the Smithsonian Astrophysical Observatory under NASA Cooperative Agreement NNX16AC86ACited by: 4.

Electronic books Conference papers and proceedings Congresses: Additional Physical Format: Print version: Carfora, Mauro. Integrable Systems and Quantum Groups. Singapore: World Scientific Publishing Co Pte Ltd, © Material Type: Document, Internet resource: Document Type: Internet Resource, Computer File: All Authors / Contributors.

Quantum group is used as the natural structure to characterize and classify rational conformal field theory [12]–[14]. Integrable lattice models are constructed and solved by quantum group theory. In Hamiltonian systems, quantum group is an enlarged symmetry that.

Quantization of Lie Groups and Lie Algebras (L D Faddeev, N Yu Reshetikhin & L A Takhtajan) Families of Commuting Transfer Matrices in q-State Vertex Models in Non-Linear Integrable Systems — Classical Theory and Quantum Theory (J H H Perk & C L Schultz) Self-Dual Solutions of the Star-Triangle Relations in Z N Models (V A Fateev & A B.

Plan: We're planning to start with Nigel Hitchin's lecture notes in the book "Integrable systems: twistors, loops groups and Riemann surfaces", and his original paper "Stable bundles and integrable systems. We then plan on covering the material in Michael Semenov-Tyan-Shansky's notes "Quantum and classical integrable 's a rough plan of the topics for individial talks.

physics and integrable 1+1 dimensional quantum field theories have very rich and. Integrable systems in quantum field theory and statistical mechanics.

Formats and Editions of Integrable systems in quantum fields theory. Integrable systems in quantum field theory and statistical mechanics.English, Book, Illustrated edition. The remainder of the book consists of three detailed expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable systems and elliptic algebras, and the groups of algebra automorphisms of quantum groups.

The preface puts the results presented in perspective. R -matrices are used to construct a set of transfer operators that describe a quantum in-tegrable system. An elaborate proof of the simultaneous diagonalizability of the transfer operators is provided.

This work largely follows a structure outlined by Pavel Etingof. Title: Quantum Dynamical R -matrices and Quantum Integrable Systems. Quantum integrable systems Depending on the interaction ranges, integrable sys- tems on a line may be classified into two groups. One contains systems with short-range interactions includ- ing the 6-function gas, the Heisenberg chain and the Toda by: 1.

The term "quantum group" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras.

Quantum Integrable Systems - CRC Press Book The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world.

Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists. Workshop on Classical and Quantum Integrable Systems (CQIS) Sunday, August 2, (All day) to Saturday, August 8, (All day) The next international Workshop on Classical and Quantum Integrable Systems (CQIS) will be held at the Omega Sirius Park Hotel and Conference Center (Sochi, Russia) on August(Sunday, Aug.

A more concise, worked example of a non-integrable system is given in the article on integrability conditions for differential systems. Some of the primary tools for studying non-integrable systems are sub-Riemannian geometry and contact 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 Pages: This book is an introduction to integrability and conformal field theory in two dimensions using quantum groups. The book begins with a brief introduction to S-matrices, spin chains and vertex models as a prelude to the study of Yang-Baxter algebras and the Bethe ansatz.

The authors then introduce the basic ideas of integrable systems, giving particular emphasis to vertex and face models. Kevin Costello - Integrable systems and quantum groups from quantum field theory Introduction to classical and quantum integrable systems by Leon Takhtajan Quantum Groups and 3.

COVID Resources. Reliable information about the coronavirus (COVID) is available from the World Health Organization (current situation, international travel).Numerous and frequently-updated resource results are available from this ’s WebJunction has pulled together information and resources to assist library staff as they consider how to handle coronavirus.

Integrable systems never-theless lead to a very interesting mathematics ranging from differential geometry and complex analysis to quantum field theory and fluid dynamics. The main reference for the course is [6]. There are other books which cover particular topics treated in the course:File Size: KB.

so-called quantum groups, which are the underlying symmetries of many relevant quantum integrable models (see, for instance [8, 10]). As it was shown in [6], Poisson coalgebras can be systematically used in order to construct completely integrable Hamiltonian systems.

Editor with Mauro Francaviglia: Integrable systems and quantum groups (CIME Lectures, Montcatini Terme, June ), Springer Verlag ; Publisher: Curves, Jacobians, and Abelian varieties, Proceedings of an AMS-IMS-SIAM Joint Summer Research Conference on the Schottky problem, AMS ; With Katrin Wendland (Eds.).

The representation theory of quantum groups is discussed, as is the function algebra approach to quantum groups, and there is a new look at the origins of quantum groups in the theory of integrable systems.

Integrable Many-Body Systems and Platonic Solids Since the mid's, it has been believed that there exist only two types of reflection groups that can generate exact solutions to quantum N-body problems with short-range interactions: A N-1 and C N.

These, respectively, allow one to solve the problem of an ensemble of atoms of identical masses. Quantum groups appeared during the eighties as the underlying algebraic symmetries of several two-dimensional integrable models. They are noncommutative generalizations of Lie groups endowed with a Hopf algebra structure, and the possibility of defining noncommutative spaces that are covariant under quantum group (co)actions soon provided a.Lie algebras, lie superalgebras, vertex algebras, and related topics: Southeastern Lie Theory Workshop Series: Categorification of Quantum Groups and Representation Theory, April, North Carolina State University: Lie Algebras, Vertex Algebras, Integrable Systems and Applications, December, College of Charleston: Noncommutative Algebraic Geometry and.The subject is interesting because it relates to the subject of quantum integrable systems in quantum mechanics.

There is an ongoing effort trying to geometrize the notion of quantum groups (as stated at page $28$ of the paper of Maulik and Okounkov). See the .