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.

Download or read book Yang Baxter Deformation of 2D Non Linear Sigma Models written by Kentaroh Yoshida and published by . This book was released on 2021 with total page 0 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. .

Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer Nature. This book was released on 2020-10-15 with total page 552 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents modern trends in the area of symmetries and their applications based on contributions to the workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2019. Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry, which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, number theory, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear partial differential operators, special functions, and others. Furthermore, the necessary tools from functional analysis are included. This is a large interdisciplinary and interrelated field. The topics covered in this volume from the workshop represent the most modern trends in the field : Representation Theory, Symmetries in String Theories, Symmetries in Gravity Theories, Supergravity, Conformal Field Theory, Integrable Systems, Polylogarithms, and Supersymmetry. They also include Supersymmetric Calogero-type models, Quantum Groups, Deformations, Quantum Computing and Deep Learning, Entanglement, Applications to Quantum Theory, and Exceptional Quantum Algebra for the standard model of particle physics This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists, including researchers and graduate students interested in Lie Theory.

Download or read book Proceedings Of The East Asia Joint Symposium On Fields And Strings 2021 written by Satoshi Iso and published by World Scientific. This book was released on 2022-06-06 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the East Asia Joint Symposium on Fields and Strings 2021, held at the Media Center of Osaka City University on November 22-27, 2021. About 160 physicists from all over East Asia attended physically or joined online this symposium and more than 50 researchers presented their results in the invited lectures, the short talks or the poster session. Quantum field theory and string theory in the context of several exciting developments were discussed, which include frontiers of supersymmetric gauge theory, anomalies and higher form symmetries, and several issues on quantum gravity and black holes.

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.

Download or read book On the Geometry of Two dimensional Anisotropic Non linear Sigma models written by and published by . This book was released on 1997 with total page 18 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book High Energy Physics Index written by and published by . This book was released on 1993 with total page 640 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Physics Briefs written by and published by . This book was released on 1994 with total page 916 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book INIS Atomindex written by and published by . This book was released on 1985 with total page 952 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book A Guide to Quantum Groups written by Vyjayanthi Chari and published by Cambridge University Press. This book was released on 1995-07-27 with total page 672 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since they first arose in the 1970s and early 1980s, quantum groups have proved to be of great interest to mathematicians and theoretical physicists. The theory of quantum groups is now well established as a fascinating chapter of representation theory, and has thrown new light on many different topics, notably low-dimensional topology and conformal field theory. The goal of this book is to give a comprehensive view of quantum groups and their applications. The authors build on a self-contained account of the foundations of the subject and go on to treat the more advanced aspects concisely and with detailed references to the literature. Thus this book can serve both as an introduction for the newcomer, and as a guide for the more experienced reader. All who have an interest in the subject will welcome this unique treatment of quantum groups.

Download or read book Studies of the Two dimensional Nonlinear Sigma model written by Thomas Henry Buscher and published by . This book was released on 1988 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mathematical Reviews written by and published by . This book was released on 2003 with total page 1432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Symmetries and Integrability of Difference Equations written by Decio Levi and published by American Mathematical Soc.. This book was released on with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book String Theory written by Joseph Gerard Polchinski and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Encyclopedia of Mathematical Physics written by Jean-Pierre Françoise and published by Academic Press. This book was released on 2006 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Encyclopedia of Mathematical Physics provides a complete resource for researchers, students and lecturers with an interest in mathematical physics. It enables readers to access basic information on topics peripheral to their own areas, to provide a repository of the core information in the area that can be used to refresh the researcher's own memory banks, and aid teachers in directing students to entries relevant to their course-work. The Encyclopedia does contain information that has been distilled, organised and presented as a complete reference tool to the user and a landmark to the body of knowledge that has accumulated in this domain. It also is a stimulus for new researchers working in mathematical physics or in areas using the methods originating from work in mathematical physics by providing them with focused high quality background information. Editorial Board: Jean-Pierre Françoise, Université Pierre et Marie Curie, Paris, France Gregory L. Naber, Drexel University, Philadelphia, PA, USA Tsou Sheung Tsun, University of Oxford, UK Also available online via ScienceDirect (2006) - featuring extensive browsing, searching, and internal cross-referencing between articles in the work, plus dynamic linking to journal articles and abstract databases, making navigation flexible and easy.

Download or read book Introduction to Classical Integrable Systems written by Olivier Babelon and published by Cambridge University Press. This book was released on 2003-04-17 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a thorough introduction to the theory of classical integrable systems, discussing the various approaches to the subject and explaining their interrelations. The book begins by introducing the central ideas of the theory of integrable systems, based on Lax representations, loop groups and Riemann surfaces. These ideas are then illustrated with detailed studies of model systems. The connection between isomonodromic deformation and integrability is discussed, and integrable field theories are covered in detail. The KP, KdV and Toda hierarchies are explained using the notion of Grassmannian, vertex operators and pseudo-differential operators. A chapter is devoted to the inverse scattering method and three complementary chapters cover the necessary mathematical tools from symplectic geometry, Riemann surfaces and Lie algebras. The book contains many worked examples and is suitable for use as a textbook on graduate courses. It also provides a comprehensive reference for researchers already working in the field.

Download or read book Integrable Quantum Field Theories written by L. Bonora and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a NATO ARW held in Como, Italy, September 14-19, 1992