Integrable Systems, Quantum Groups, and Quantum Field Theories PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download Integrable Systems, Quantum Groups, and Quantum Field Theories PDF full book. Access full book title Integrable Systems, Quantum Groups, and Quantum Field Theories by Alberto Ibort. Download full books in PDF and EPUB format.
Author: Alberto Ibort Publisher: Springer Science & Business Media ISBN: 9401119805 Category : Science Languages : en Pages : 508
Book Description
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.
Author: Alberto Ibort Publisher: Springer Science & Business Media ISBN: 9401119805 Category : Science Languages : en Pages : 508
Book Description
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.
Author: Mo-lin Ge Publisher: World Scientific ISBN: 9814555835 Category : Languages : en Pages : 242
Book Description
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.
Author: Mauro Carfora Publisher: World Scientific ISBN: 9814554766 Category : Languages : en Pages : 194
Book Description
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.
Author: Mo-Lin Ge Publisher: World Scientific ISBN: 9814551198 Category : Languages : en Pages : 208
Book Description
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:
Author: Atsuo Kuniba Publisher: Springer Nature ISBN: 981193262X Category : Science Languages : en Pages : 330
Book Description
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.
Author: S. Pakuliak Publisher: Springer Science & Business Media ISBN: 9401006709 Category : Science Languages : en Pages : 334
Book Description
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.
Author: Ron Donagi Publisher: Springer ISBN: 3540477063 Category : Mathematics Languages : en Pages : 496
Book Description
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.
Author: Asesh Roy Chowdhury Publisher: CRC Press ISBN: 0203498011 Category : Science Languages : en Pages : 425
Book Description
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 alike, and none offer a systematic survey of the m
Author: J.J. Duistermaat Publisher: Springer ISBN: 9780387566238 Category : Mathematics Languages : en Pages : 0
Book Description
This book is devoted to Quisped, Roberts, and Thompson (QRT) maps, considered as automorphisms of rational elliptic surfaces. The theory of QRT maps arose from problems in mathematical physics, involving difference equations. The application of QRT maps to these and other problems in the literature, including Poncelet mapping and the elliptic billiard, is examined in detail. The link between elliptic fibrations and completely integrable Hamiltonian systems is also discussed. The book begins with a comprehensive overview of the subject, including QRT maps, singularity confinement, automorphisms of rational elliptic surfaces, action on homology classes, and periodic QRT maps. Later chapters cover these topics and more in detail. While QRT maps will be familiar to specialists in algebraic geometry, the present volume makes the subject accessible to mathematicians and graduate students in a classroom setting or for self-study.
Author: Alberto Ibort
Author: Alberto Ibort
Author: Mo-lin Ge
Author: M. Jimbo
Author: Mauro Carfora
Author: Mo-Lin Ge
Author: Atsuo Kuniba
Author: S. Pakuliak
Author: Ron Donagi
Author: Asesh Roy Chowdhury
Author: J.J. Duistermaat