Integrable Systems Quantum Groups And Quantum Field Theories

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Integrable Systems, Quantum Groups, and Quantum Field Theories

Alberto Ibort,M.A. Rodríguez
Integrable Systems Quantum Groups and Quantum Field Theories Book PDF

Author : Alberto Ibort,M.A. Rodríguez
Publisher : Springer Science & Business Media
Page : 508 pages
File Size : 44,8 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401119801

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Integrable Systems, Quantum Groups, and Quantum Field Theories by Alberto Ibort,M.A. Rodríguez Pdf

In many ways the last decade has witnessed a surge of interest in the interplay between theoretical physics and some traditional areas of pure mathematics. This book contains the lectures delivered at the NATO-ASI Summer School on `Recent Problems in Mathematical Physics' held at Salamanca, Spain (1992), offering a pedagogical and updated approach to some of the problems that have been at the heart of these events. 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. Apart from these, traditional and new problems in quantum gravity are reviewed. Other contributions to the School included in the book range from symmetries in partial differential equations to geometrical phases in quantum physics. The book is addressed to researchers in the fields covered, PhD students and any scientist interested in obtaining an updated view of the subjects.

Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics

Mo-lin Ge
Quantum Group And Quantum Integrable Systems Nankai Lectures On Mathematical Physics Book PDF

Author : Mo-lin Ge
Publisher : World Scientific
Page : 242 pages
File Size : 51,7 Mb
Release : 1992-05-30
Category : Electronic
ISBN : 9789814555838

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Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics by Mo-lin Ge Pdf

This volume contains the lectures given by the three speakers, M Jimbo, P P Kulish and E K Sklyanin, who are outstanding experts in their field. It is essential reading to those working in the fields of Quantum Groups, and Integrable Systems.

Integrable Systems in Quantum Field Theory and Statistical Mechanics

M. Jimbo,T. Miwa,A. Tsuchiya
Integrable Systems in Quantum Field Theory and Statistical Mechanics Book PDF

Author : M. Jimbo,T. Miwa,A. Tsuchiya
Publisher : Elsevier
Page : 695 pages
File Size : 52,5 Mb
Release : 2014-05-19
Category : Science
ISBN : 9781483295251

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Integrable Systems in Quantum Field Theory and Statistical Mechanics by M. Jimbo,T. Miwa,A. Tsuchiya Pdf

Integrable Sys Quantum Field Theory

Integrable Systems And Quantum Groups

Mauro Carfora,Maurizio Martellini,Annalisa Marzuoli
Integrable Systems And Quantum Groups Book PDF

Author : Mauro Carfora,Maurizio Martellini,Annalisa Marzuoli
Publisher : World Scientific
Page : 194 pages
File Size : 41,8 Mb
Release : 1992-04-30
Category : Electronic
ISBN : 9789814554763

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Integrable Systems And Quantum Groups by Mauro Carfora,Maurizio Martellini,Annalisa Marzuoli Pdf

This volume contains lectures on recent advances in the theory of integrable systems and quantum groups. It introduces the reader to attractive areas of current research.

Quantum Groups in Three-Dimensional Integrability

Atsuo Kuniba
Quantum Groups in Three Dimensional Integrability Book PDF

Author : Atsuo Kuniba
Publisher : Springer Nature
Page : 330 pages
File Size : 48,7 Mb
Release : 2022-09-25
Category : Science
ISBN : 9789811932625

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Quantum Groups in Three-Dimensional Integrability by Atsuo Kuniba Pdf

Quantum groups have been studied intensively in mathematics and have found many valuable applications in theoretical and mathematical physics since their discovery in the mid-1980s. Roughly speaking, there are two prototype examples of quantum groups, denoted by Uq and Aq. The former is a deformation of the universal enveloping algebra of a Kac–Moody Lie algebra, whereas the latter is a deformation of the coordinate ring of a Lie group. Although they are dual to each other in principle, most of the applications so far are based on Uq, and the main targets are solvable lattice models in 2-dimensions or quantum field theories in 1+1 dimensions. This book aims to present a unique approach to 3-dimensional integrability based on Aq. It starts from the tetrahedron equation, a 3-dimensional analogue of the Yang–Baxter equation, and its solution due to work by Kapranov–Voevodsky (1994). Then, it guides readers to its variety of generalizations, relations to quantum groups, and applications. They include a connection to the Poincaré–Birkhoff–Witt basis of a unipotent part of Uq, reductions to the solutions of the Yang–Baxter equation, reflection equation, G2 reflection equation, matrix product constructions of quantum R matrices and reflection K matrices, stationary measures of multi-species simple-exclusion processes, etc. These contents of the book are quite distinct from conventional approaches and will stimulate and enrich the theories of quantum groups and integrable systems.

Introduction to Quantum Group and Integrable Massive Models of Quantum Field Theory

Mo-Lin Ge,Bao-Heng Zhao
Introduction to Quantum Group and Integrable Massive Models of Quantum Field Theory Book PDF

Author : Mo-Lin Ge,Bao-Heng Zhao
Publisher : World Scientific
Page : 208 pages
File Size : 55,5 Mb
Release : 1990-09-24
Category : Electronic
ISBN : 9789814551199

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Introduction to Quantum Group and Integrable Massive Models of Quantum Field Theory by Mo-Lin Ge,Bao-Heng Zhao Pdf

The Proceedings consists of 6 lectures each from Prof L Takhtajan and Prof F Smirnov which were presented during the workshop. Contents:Lectures on Integrable Massive Models of Quantum Field Theory (F A Smirnov):General Problems of the Quantum Field Theory. Completely Integrable ModelsSpace of States. Form Factors. A Set of Axioms for Form FactorsLocal Commutativity and Asymptotic ConditionsForm Factors in SU(2)-Invariant Thirring ModelNecessary Properties of the Currents Form Factors in SU(2)-Invariant Thirring ModelProperties of Currents in SU(2)-Invariant Thirring ModelLectures on Quantum Groups (L A Takhtajan):Historical Introduction. Algebraic BackgroundPoisson-Lie Groups, CYBE and Modified CYBE. Connection with ISM. Lie-Algebraic Meaning of CYBE and Modified CYBEQuantization Procedure as a Deformation of the Algebra of Classical ObservablesWeyl Quantization. Quantization of Poisson-Lie Groups Associated with CYBEQYBEQuantization of Poisson-Lie Groups Associated with Modified CYBE. Quantum Matrix Algebras. Quantum Determinant and Quantum Groups SL(n) and GL (n)Quantum Vector Spaces for the Quantum Groups SLq(n), GLq(n) and their Real Forms. Quantum Groups Oq(N), SPq(n), Quantum Vector Spaces Associated with them and their Real FormsQuantization of the Universal Enveloping Algebras of the Simple Lie Algebras. Elements of the Representations Theory Readership: Mathematical physicists. keywords:

Quantum Groups, Quantum Categories and Quantum Field Theory

Jürg Fröhlich,Thomas Kerler
Quantum Groups Quantum Categories and Quantum Field Theory Book PDF

Author : Jürg Fröhlich,Thomas Kerler
Publisher : Springer
Page : 438 pages
File Size : 49,7 Mb
Release : 2006-11-15
Category : Mathematics
ISBN : 9783540476115

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Quantum Groups, Quantum Categories and Quantum Field Theory by Jürg Fröhlich,Thomas Kerler Pdf

This book reviews recent results on low-dimensional quantum field theories and their connection with quantum group theory and the theory of braided, balanced tensor categories. It presents detailed, mathematically precise introductions to these subjects and then continues with new results. Among the main results are a detailed analysis of the representation theory of U (sl ), for q a primitive root of unity, and a semi-simple quotient thereof, a classfication of braided tensor categories generated by an object of q-dimension less than two, and an application of these results to the theory of sectors in algebraic quantum field theory. This clarifies the notion of "quantized symmetries" in quantum fieldtheory. The reader is expected to be familiar with basic notions and resultsin algebra. The book is intended for research mathematicians, mathematical physicists and graduate students.

Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory

S. Pakuliak,G. von Gehlen
Integrable Structures of Exactly Solvable Two Dimensional Models of Quantum Field Theory Book PDF

Author : S. Pakuliak,G. von Gehlen
Publisher : Springer Science & Business Media
Page : 334 pages
File Size : 41,5 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401006705

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Integrable Structures of Exactly Solvable Two-Dimensional Models of Quantum Field Theory by S. Pakuliak,G. von Gehlen Pdf

Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.

Integrable Systems and Quantum Groups

Ron Donagi,Boris Dubrovin,Edward Frenkel,Emma Previato
Integrable Systems and Quantum Groups Book PDF

Author : Ron Donagi,Boris Dubrovin,Edward Frenkel,Emma Previato
Publisher : Springer
Page : 496 pages
File Size : 40,7 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540477068

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Integrable Systems and Quantum Groups by Ron Donagi,Boris Dubrovin,Edward Frenkel,Emma Previato Pdf

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. The papers contained in this volume have at the same time the character of survey articles and of research papers, since they contain both a survey of current problems and a number of original contributions to the subject.

Quantum Theory, Deformation and Integrability

R. Carroll
Quantum Theory Deformation and Integrability Book PDF

Author : R. Carroll
Publisher : Elsevier
Page : 420 pages
File Size : 43,8 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.

The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems

Pavel Etingof,Pavel I. Etingof,Frederic Latour
The Dynamical Yang Baxter Equation Representation Theory and Quantum Integrable Systems Book PDF

Author : Pavel Etingof,Pavel I. Etingof,Frederic Latour
Publisher : Oxford University Press on Demand
Page : 151 pages
File Size : 43,8 Mb
Release : 2005
Category : Mathematics
ISBN : 9780198530688

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The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems by Pavel Etingof,Pavel I. Etingof,Frederic Latour Pdf

The text is based on an established graduate course given at MIT that provides an introduction to the theory of the dynamical Yang-Baxter equation and its applications, which is an important area in representation theory and quantum groups. The book, which contains many detailed proofs and explicit calculations, will be accessible to graduate students of mathematics, who are familiar with the basics of representation theory of semisimple Lie algebras.

Particles and Fields

Gordon W. Semenoff,Luc Vinet
Particles and Fields Book PDF

Author : Gordon W. Semenoff,Luc Vinet
Publisher : Springer Science & Business Media
Page : 501 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Science
ISBN : 9781461214106

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Particles and Fields by Gordon W. Semenoff,Luc Vinet Pdf

The focus of this volume is on quantum field theory: inegrable theories, statistical systems, and applications to condensed-matter physics. It covers some of the most significant recent advances in theoretical physics at a level accessible to advanced graduate students. The contributions, each by a noted researcher, dicuss such topics as: some remarkable features of integrable Toda field theories (E. Corrigan), properties of a gas of interacting Fermions in a lattice of magnetic ions (J. Feldman &. al.), how quantum groups arise in three-dimensional topological quantum field thory (D. Freed), a method for computing correlation functions of solvable lattice models (T. Miwa), matrix models discussed from the point of view of integrable systems (A. Morozov), localization of path integrals in certain equivariant cohomologies (A. Niemi), Calogero-Moser systems (S. Ruijsenaars), planar gauge theories with broken symmetries (M. de Wild Propitius & F.A. Bais), quantum-Hall fluids (A. Capelli & al.), spectral theory of quantum vortex operators (P.I. Ettinghoff).

Quantum Groups, Integrable Models And Statistiacal Systems

Jean Letourneux,Luc Vinet
Quantum Groups Integrable Models And Statistiacal Systems Book PDF

Author : Jean Letourneux,Luc Vinet
Publisher : World Scientific
Page : 302 pages
File Size : 46,7 Mb
Release : 1993-12-22
Category : Electronic
ISBN : 9789814552417

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Quantum Groups, Integrable Models And Statistiacal Systems by Jean Letourneux,Luc Vinet Pdf

This volume contains the lectures presented at the workshop on “Quantum Groups, Integrable Models and Statistical Systems”. The papers give either a full exposition of original results or a review of fundamental aspects of this most active research area.

Proceedings of the International Congress of Mathematicians

S.D. Chatterji
Proceedings of the International Congress of Mathematicians Book PDF

Author : S.D. Chatterji
Publisher : Birkhäuser
Page : 1669 pages
File Size : 50,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034890786

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Proceedings of the International Congress of Mathematicians by S.D. Chatterji Pdf

Since the first ICM was held in Zürich in 1897, it has become the pinnacle of mathematical gatherings. It aims at giving an overview of the current state of different branches of mathematics and its applications as well as an insight into the treatment of special problems of exceptional importance. The proceedings of the ICMs have provided a rich chronology of mathematical development in all its branches and a unique documentation of contemporary research. They form an indispensable part of every mathematical library. The Proceedings of the International Congress of Mathematicians 1994, held in Zürich from August 3rd to 11th, 1994, are published in two volumes. Volume I contains an account of the organization of the Congress, the list of ordinary members, the reports on the work of the Fields Medalists and the Nevanlinna Prize Winner, the plenary one-hour addresses, and the invited addresses presented at Section Meetings 1 - 6. Volume II contains the invited address for Section Meetings 7 - 19. A complete author index is included in both volumes. '...the content of these impressive two volumes sheds a certain light on the present state of mathematical sciences and anybody doing research in mathematics should look carefully at these Proceedings. For young people beginning research, this is even more important, so these are a must for any serious mathematics library. The graphical presentation is, as always with Birkhäuser, excellent....' (Revue Roumaine de Mathematiques pures et Appliquées)

Introduction to Quantum Groups

Masud Chaichian,Andrei Pavlovich Demichev
Introduction to Quantum Groups Book PDF

Author : Masud Chaichian,Andrei Pavlovich Demichev
Publisher : World Scientific
Page : 362 pages
File Size : 53,6 Mb
Release : 1996
Category : Science
ISBN : 9810226233

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Introduction to Quantum Groups by Masud Chaichian,Andrei Pavlovich Demichev Pdf

In the past decade there has been an extemely rapid growth in the interest and development of quantum group theory.This book provides students and researchers with a practical introduction to the principal ideas of quantum groups theory and its applications to quantum mechanical and modern field theory problems. It begins with a review of, and introduction to, the mathematical aspects of quantum deformation of classical groups, Lie algebras and related objects (algebras of functions on spaces, differential and integral calculi). In the subsequent chapters the richness of mathematical structure and power of the quantum deformation methods and non-commutative geometry is illustrated on the different examples starting from the simplest quantum mechanical system — harmonic oscillator and ending with actual problems of modern field theory, such as the attempts to construct lattice-like regularization consistent with space-time Poincaré symmetry and to incorporate Higgs fields in the general geometrical frame of gauge theories. Graduate students and researchers studying the problems of quantum field theory, particle physics and mathematical aspects of quantum symmetries will find the book of interest.