Yang Baxter Equation In Integrable Systems

Author : Michio Jimbo
Publisher : World Scientific
ISBN 13 : 9789810201210
Total Pages : 740 pages
Book Rating : 4.14/5 ( download)

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Download or read book Yang-Baxter Equation in Integrable Systems written by Michio Jimbo and published by World Scientific. This book was released on 1990 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.

Author : Pavel Etingof
Publisher : OUP Oxford
ISBN 13 : 0191523925
Total Pages : 152 pages
Book Rating : 4.22/5 ( download)

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Download or read book The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems written by Pavel Etingof and published by OUP Oxford. This book was released on 2005-03-24 with total page 152 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : P. I. Etingof
Publisher :
ISBN 13 :
Total Pages : 138 pages
Book Rating : 4.50/5 ( download)

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Download or read book The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems written by P. I. Etingof and published by . This book was released on 2005 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Kentaroh Yoshida
Publisher : Springer Nature
ISBN 13 : 9811617031
Total Pages : 79 pages
Book Rating : 4.34/5 ( download)

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Download or read book Yang–Baxter Deformation of 2D Non-Linear Sigma Models written by Kentaroh Yoshida and published by Springer Nature. This book was released on 2021-06-03 with total page 79 pages. Available in PDF, EPUB and Kindle. Book excerpt: In mathematical physics, one of the fascinating issues is the study of integrable systems. In particular, non-perturbative techniques that have been developed have triggered significant insight for real physics. There are basically two notions of integrability: classical integrability and quantum integrability. In this book, the focus is on the former, classical integrability. When the system has a finite number of degrees of freedom, it has been well captured by the Arnold–Liouville theorem. However, when the number of degrees of freedom is infinite, as in classical field theories, the integrable structure is enriched profoundly. In fact, the study of classically integrable field theories has a long history and various kinds of techniques, including the classical inverse scattering method, which have been developed so far. In previously published books, these techniques have been collected and well described and are easy to find in traditional, standard textbooks. One of the intriguing subjects in classically integrable systems is the investigation of deformations preserving integrability. Usually, it is not considered systematic to perform such a deformation, and one must study systems case by case and show the integrability of the deformed systems by constructing the associated Lax pair or action-angle variables. Recently, a new, systematic method to perform integrable deformations of 2D non-linear sigma models was developed. It was invented by C. Klimcik in 2002, and the integrability of the deformed sigma models was shown in 2008. The original work was done for 2D principal chiral models, but it has been generalized in various directions nowadays. In this book, the recent progress on this Yang–Baxter deformation is described in a pedagogical manner, including some simple examples. Applications of Yang–Baxter deformation to string theory are also described briefly.

Author : Mauro Carfora
Publisher : World Scientific
ISBN 13 : 9814554766
Total Pages : 194 pages
Book Rating : 4.63/5 ( download)

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Download or read book Integrable Systems And Quantum Groups written by Mauro Carfora and published by World Scientific. This book was released on 1992-04-30 with total page 194 pages. 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.

Author : Mo-lin Ge
Publisher : World Scientific
ISBN 13 : 9814555835
Total Pages : 242 pages
Book Rating : 4.38/5 ( download)

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Download or read book Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics written by Mo-lin Ge and published by World Scientific. This book was released on 1992-05-30 with total page 242 pages. 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.

Author : Pavel Etingof
Publisher : Oxford University Press on Demand
ISBN 13 : 0198530684
Total Pages : 151 pages
Book Rating : 4.88/5 ( download)

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Download or read book The Dynamical Yang-Baxter Equation, Representation Theory, and Quantum Integrable Systems written by Pavel Etingof and published by Oxford University Press on Demand. This book was released on 2005 with total page 151 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : A Kundu
Publisher : CRC Press
ISBN 13 : 9781420034615
Total Pages : 320 pages
Book Rating : 4.18/5 ( download)

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Download or read book Classical and Quantum Nonlinear Integrable Systems written by A Kundu and published by CRC Press. This book was released on 2019-04-23 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covering both classical and quantum models, nonlinear integrable systems are of considerable theoretical and practical interest, with applications over a wide range of topics, including water waves, pin models, nonlinear optics, correlated electron systems, plasma physics, and reaction-diffusion processes. Comprising one part on classical theories

Author : Michio Jimbo
Publisher : World Scientific
ISBN 13 : 9789810201203
Total Pages : 740 pages
Book Rating : 4.06/5 ( download)

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Download or read book Yang-Baxter Equation in Integrable Systems written by Michio Jimbo and published by World Scientific. This book was released on 1990 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.

Author : Florin Felix Nichita
Publisher :
ISBN 13 : 9783038973256
Total Pages : 1 pages
Book Rating : 4.54/5 ( download)

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Download or read book Hopf Algebras, Quantum Groups and Yang-Baxter Equations written by Florin Felix Nichita and published by . This book was released on 2019 with total page 1 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Yang-Baxter equation first appeared in theoretical physics, in a paper by the Nobel laureate C.N. Yang and in the work of R.J. Baxter in the field of Statistical Mechanics. At the 1990 International Mathematics Congress, Vladimir Drinfeld, Vaughan F. R. Jones, and Edward Witten were awarded Fields Medals for their work related to the Yang-Baxter equation. It turned out that this equation is one of the basic equations in mathematical physics; more precisely, it is used for introducing the theory of quantum groups. It also plays a crucial role in: knot theory, braided categories, the analysis of integrable systems, non-commutative descent theory, quantum computing, non-commutative geometry, etc. Many scientists have used the axioms of various algebraic structures (quasi-triangular Hopf algebras, Yetter-Drinfeld categories, quandles, group actions, Lie (super)algebras, brace structures, (co)algebra structures, Jordan triples, Boolean algebras, relations on sets, etc.) or computer calculations (and Grobner bases) in order to produce solutions for the Yang-Baxter equation. However, the full classification of its solutions remains an open problem. At present, the study of solutions of the Yang-Baxter equation attracts the attention of a broad circle of scientists. The current volume highlights various aspects of the Yang-Baxter equation, related algebraic structures, and applications.