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Integrable Systems, Quantum Groups, and Quantum Field Theories

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 805/5 ( reviews)

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Book Synopsis Integrable Systems, Quantum Groups, and Quantum Field Theories by : Alberto Ibort

Download or read book Integrable Systems, Quantum Groups, and Quantum Field Theories written by Alberto Ibort. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Integrable Systems in Quantum Field Theory and Statistical Mechanics

2014-05-19 Science
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Release : 2014-05-19
Genre : Science
Kind : eBook
Book Rating : 257/5 ( reviews)

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Book Synopsis Integrable Systems in Quantum Field Theory and Statistical Mechanics by : M. Jimbo

Download or read book Integrable Systems in Quantum Field Theory and Statistical Mechanics written by M. Jimbo. This book was released on 2014-05-19. Available in PDF, EPUB and Kindle. Book excerpt: Integrable Sys Quantum Field Theory

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

1992-05-30
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Release : 1992-05-30
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Kind : eBook
Book Rating : 835/5 ( reviews)

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Book Synopsis Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics by : Mo-lin Ge

Download or read book Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics written by Mo-lin Ge. This book was released on 1992-05-30. Available in PDF, EPUB and Kindle. Book excerpt: 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 And Quantum Groups

1992-04-30
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Release : 1992-04-30
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Kind : eBook
Book Rating : 766/5 ( reviews)

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Book Synopsis Integrable Systems And Quantum Groups by : Mauro Carfora

Download or read book Integrable Systems And Quantum Groups written by Mauro Carfora. This book was released on 1992-04-30. Available in PDF, EPUB and Kindle. Book excerpt: 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

2022-09-25 Science
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Release : 2022-09-25
Genre : Science
Kind : eBook
Book Rating : 62X/5 ( reviews)

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Book Synopsis Quantum Groups in Three-Dimensional Integrability by : Atsuo Kuniba

Download or read book Quantum Groups in Three-Dimensional Integrability written by Atsuo Kuniba. This book was released on 2022-09-25. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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