Quantum Groups, Integrable Models And Statistiacal Systems PDF Download

Author: Jean Letourneux
Publisher: World Scientific
ISBN: 9814552410
Category :
Languages : en
Pages : 302

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Book Description
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.

Author: Alberto Ibort
Publisher: Springer Science & Business Media
ISBN: 9401119805
Category : Science
Languages : en
Pages : 508

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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: M. Jimbo
Publisher: Elsevier
ISBN: 1483295257
Category : Science
Languages : en
Pages : 695

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Book Description
Integrable Sys Quantum Field Theory

Author: Jean LeTourneux
Publisher: World Scientific Publishing Company Incorporated
ISBN: 9789810215552
Category : Science
Languages : en
Pages : 290

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Book Description

Author: Mauro Carfora
Publisher: World Scientific
ISBN: 9814554766
Category :
Languages : en
Pages : 194

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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: 9814549754
Category :
Languages : en
Pages : 186

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Book Description
This volume covers the recent developments of the exact solvable models, Yangian symmetry, the long-ranged interaction models and high-dimensional integrable systems. The authors are all experts in their fields. The volume provides a systematic introduction to statistical and mathematical physics and contains review papers and other contributions.

Author: Mo-lin Ge
Publisher: World Scientific
ISBN: 9814602566
Category :
Languages : en
Pages : 352

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Book Description
The lectures in this volume discuss topics in statistical mechanics, the geometric and algebraic approaches to q-deformation theories, two-dimensional gravity and related problems of mathematical physics, including Vassiliev invariants and the Jones polynomials, the R-matrix with Z-symmetry, reflection equations and quantum algebra, W-geometry, braid linear algebra, holomorphic q-difference systems and q-Poincaré algebra.

Author: Mo-lin Ge
Publisher: World Scientific
ISBN: 9814555835
Category :
Languages : en
Pages : 242

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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: Michio Jimbo
Publisher: American Mathematical Soc.
ISBN: 1470465523
Category : Education
Languages : en
Pages : 192

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Book Description
Integrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published monograph on this subject. It treats integrable lattice models, notably the six-vertex model and the XXZ Heisenberg spin chain. A pair of fermions is introduced and used to create a basis of the space of local operators, leading to the result that all correlation functions at finite distances are expressible in terms of two transcendental functions with rational coefficients. Step-by-step explanations are given for all materials necessary for this construction, ranging from algebraic Bethe ansatz, representations of quantum groups, and the Bazhanov-Lukyanov-Zamolodchikov construction in conformal field theory to Riemann surfaces and their Jacobians. Several examples and applications are given along with numerical results. Going through the book, readers will find themselves at the forefront of this rapidly developing research field.

Author: Atsuo Kuniba
Publisher: Springer Nature
ISBN: 981193262X
Category : Science
Languages : en
Pages : 330

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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.