Integrable Systems Quantum Groups And Quantum Field Theories
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Integrable Systems Quantum Groups And Quantum Field Theories
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Author : Alberto Ibort
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Systems Quantum Groups And Quantum Field Theories written by Alberto Ibort and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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
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Author : Mo-lin Ge
language : en
Publisher: World Scientific
Release Date : 1992-05-30
Quantum Group And Quantum Integrable Systems Nankai Lectures On Mathematical Physics written by Mo-lin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-05-30 with categories.
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
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Author : M. Jimbo
language : en
Publisher: Elsevier
Release Date : 2014-05-19
Integrable Systems In Quantum Field Theory And Statistical Mechanics written by M. Jimbo and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-19 with Science categories.
Integrable Sys Quantum Field Theory
Integrable Systems And Quantum Groups
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Author : Mauro Carfora
language : en
Publisher: World Scientific
Release Date : 1992-04-30
Integrable Systems And Quantum Groups written by Mauro Carfora and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-04-30 with categories.
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
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Author : Atsuo Kuniba
language : en
Publisher: Springer Nature
Release Date : 2022-09-25
Quantum Groups In Three Dimensional Integrability written by Atsuo Kuniba and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-09-25 with Science categories.
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
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Author : Mo-Lin Ge
language : en
Publisher: World Scientific
Release Date : 1990-09-24
Introduction To Quantum Group And Integrable Massive Models Of Quantum Field Theory written by Mo-Lin Ge and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-09-24 with categories.
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:
Integrable Structures Of Exactly Solvable Two Dimensional Models Of Quantum Field Theory
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Author : S. Pakuliak
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Integrable Structures Of Exactly Solvable Two Dimensional Models Of Quantum Field Theory written by S. Pakuliak and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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.
Quantum Theory Deformation And Integrability
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Author : R. Carroll
language : en
Publisher: Elsevier
Release Date : 2000-11-09
Quantum Theory Deformation And Integrability written by R. Carroll and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-11-09 with Science categories.
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.
Integrable Systems And Quantum Groups
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Author : Ron Donagi
language : en
Publisher: Springer
Release Date : 2006-11-14
Integrable Systems And Quantum Groups written by Ron Donagi and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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.
Particles And Fields
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Author : Gordon W. Semenoff
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Particles And Fields written by Gordon W. Semenoff and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.
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).