Download or read book Symmetries Integrable Systems and Representations written by Kenji Iohara and published by Springer. This book was released on 2012-12-05 with total page 638 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Download or read book Symmetries Integrable Systems and Representations written by Kenji Iohara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is the result of two international workshops; Infinite Analysis 11 – Frontier of Integrability – held at University of Tokyo, Japan in July 25th to 29th, 2011, and Symmetries, Integrable Systems and Representations held at Université Claude Bernard Lyon 1, France in December 13th to 16th, 2011. Included are research articles based on the talks presented at the workshops, latest results obtained thereafter, and some review articles. The subjects discussed range across diverse areas such as algebraic geometry, combinatorics, differential equations, integrable systems, representation theory, solvable lattice models and special functions. Through these topics, the reader will find some recent developments in the field of mathematical physics and their interactions with several other domains.

Download or read book Symmetries and Integrability of Difference Equations written by Peter A. Clarkson and published by Cambridge University Press. This book was released on 1999-02-04 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises state-of-the-art articles in discrete integrable systems.

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 1996 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to a topic that has undergone rapid and fruitful development over the last few years: symmetries and integrability of difference equations and q-difference equations and the theory of special functions that occur as solutions of such equations. Techniques that have been traditionally applied to solve linear and nonlinear differential equations are now being successfully adapted and applied to discrete equations. This volume is based on contributions made by leading experts in the field during the workshop on Symmetries and Integrability of Difference Equations held Estérel, Québec, in May 1994. Giving an up-to-date review of the current status of the field, the book treats these specific topics: Lie group and quantum group symmetries of difference and q-difference equations, integrable and nonintegrable discretizations of continuous integrable systems, integrability of difference equations, discrete Painlevé property and singularity confinement, integrable mappings, applications in statistical mechanics and field theories, Yang-Baxter equations, q-special functions and discrete polynomials, and q-difference integrable systems.

Download or read book Field Theory Integrable Systems and Symmetries written by Faqir Chand Khanna and published by Publications CRM. This book was released on 1997 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Representation Theory Mathematical Physics and Integrable Systems written by Anton Alekseev and published by Springer Nature. This book was released on 2022-02-05 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the course of his distinguished career, Nicolai Reshetikhin has made a number of groundbreaking contributions in several fields, including representation theory, integrable systems, and topology. The chapters in this volume – compiled on the occasion of his 60th birthday – are written by distinguished mathematicians and physicists and pay tribute to his many significant and lasting achievements. Covering the latest developments at the interface of noncommutative algebra, differential and algebraic geometry, and perspectives arising from physics, this volume explores topics such as the development of new and powerful knot invariants, new perspectives on enumerative geometry and string theory, and the introduction of cluster algebra and categorification techniques into a broad range of areas. Chapters will also cover novel applications of representation theory to random matrix theory, exactly solvable models in statistical mechanics, and integrable hierarchies. The recent progress in the mathematical and physicals aspects of deformation quantization and tensor categories is also addressed. Representation Theory, Mathematical Physics, and Integrable Systems will be of interest to a wide audience of mathematicians interested in these areas and the connections between them, ranging from graduate students to junior, mid-career, and senior researchers.

Download or read book Symmetries of Maxwell s Equations written by W.I. Fushchich and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the fina\ question. G. K. Chesterton. The Scandal of Father 'The Hermit Oad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gu\ik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.

Download or read book Symmetries in Science V written by Bruno Gruber and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of a symposium held in Landesbildungszentrum Schloss Hofen, Lochau, Vorarlberg, Austria, July 30-August 3, 1990

Download or read book Groups and Symmetries written by Yvette Kosmann-Schwarzbach and published by Springer Science & Business Media. This book was released on 2009-10-16 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: - Combines material from many areas of mathematics, including algebra, geometry, and analysis, so students see connections between these areas - Applies material to physics so students appreciate the applications of abstract mathematics - Assumes only linear algebra and calculus, making an advanced subject accessible to undergraduates - Includes 142 exercises, many with hints or complete solutions, so text may be used in the classroom or for self study

Download or read book The Schr dinger Virasoro Algebra written by Jérémie Unterberger and published by Springer Science & Business Media. This book was released on 2011-10-25 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph provides the first up-to-date and self-contained presentation of a recently discovered mathematical structure—the Schrödinger-Virasoro algebra. Just as Poincaré invariance or conformal (Virasoro) invariance play a key rôle in understanding, respectively, elementary particles and two-dimensional equilibrium statistical physics, this algebra of non-relativistic conformal symmetries may be expected to apply itself naturally to the study of some models of non-equilibrium statistical physics, or more specifically in the context of recent developments related to the non-relativistic AdS/CFT correspondence. The study of the structure of this infinite-dimensional Lie algebra touches upon topics as various as statistical physics, vertex algebras, Poisson geometry, integrable systems and supergeometry as well as representation theory, the cohomology of infinite-dimensional Lie algebras, and the spectral theory of Schrödinger operators.

Download or read book GROUP 24 written by J.P Gazeau and published by CRC Press. This book was released on 2003-11-30 with total page 968 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most enduring elements in theoretical physics has been group theory. GROUP 24: Physical and Mathematical Aspects of Symmetries provides an important selection of informative articles describing recent advances in the field. The applications of group theory presented in this book deal not only with the traditional fields of physics, but a

Download or read book Elements of Classical and Quantum Integrable Systems written by Gleb Arutyunov and published by Springer. This book was released on 2019-07-23 with total page 414 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable models have a fascinating history with many important discoveries that dates back to the famous Kepler problem of planetary motion. Nowadays it is well recognised that integrable systems play a ubiquitous role in many research areas ranging from quantum field theory, string theory, solvable models of statistical mechanics, black hole physics, quantum chaos and the AdS/CFT correspondence, to pure mathematics, such as representation theory, harmonic analysis, random matrix theory and complex geometry. Starting with the Liouville theorem and finite-dimensional integrable models, this book covers the basic concepts of integrability including elements of the modern geometric approach based on Poisson reduction, classical and quantum factorised scattering and various incarnations of the Bethe Ansatz. Applications of integrability methods are illustrated in vast detail on the concrete examples of the Calogero-Moser-Sutherland and Ruijsenaars-Schneider models, the Heisenberg spin chain and the one-dimensional Bose gas interacting via a delta-function potential. This book has intermediate and advanced topics with details to make them clearly comprehensible.

Download or read book Lie Algebraic Methods in Integrable Systems written by Amit K. Roy-Chowdhury and published by CRC Press. This book was released on 2021-01-04 with total page 372 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last thirty years, the subject of nonlinear integrable systems has grown into a full-fledged research topic. In the last decade, Lie algebraic methods have grown in importance to various fields of theoretical research and worked to establish close relations between apparently unrelated systems. The various ideas associated with Lie algebra and Lie groups can be used to form a particularly elegant approach to the properties of nonlinear systems. In this volume, the author exposes the basic techniques of using Lie algebraic concepts to explore the domain of nonlinear integrable systems. His emphasis is not on developing a rigorous mathematical basis, but on using Lie algebraic methods as an effective tool. The book begins by establishing a practical basis in Lie algebra, including discussions of structure Lie, loop, and Virasor groups, quantum tori and Kac-Moody algebras, and gradation. It then offers a detailed discussion of prolongation structure and its representation theory, the orbit approach-for both finite and infinite dimension Lie algebra. The author also presents the modern approach to symmetries of integrable systems, including important new ideas in symmetry analysis, such as gauge transformations, and the "soldering" approach. He then moves to Hamiltonian structure, where he presents the Drinfeld-Sokolov approach, the Lie algebraic approach, Kupershmidt's approach, Hamiltonian reductions and the Gelfand Dikii formula. He concludes his treatment of Lie algebraic methods with a discussion of the classical r-matrix, its use, and its relations to double Lie algebra and the KP equation.

Download or read book Generalized Symmetries In Physics Proceedings Of The International Symposium On Mathematical Physics written by Heinz-dietrich Doebner and published by World Scientific. This book was released on 1994-07-05 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains material submitted to a symposium on mathematical physics in July 1993 at the Technical University of Clausthal. It focuses on mathematical and physical notions of symmetries, especially on generalized and quantum symmetries (quantum groups and algebras) with applications to integrable systems, quasi-exact solvability, quantization methods and nonlinear problems. The workshop is a continuation of the series of meetings and workshops on mathematical physics in Clausthal which brings together mathematicians, theoretical and mathematical physicists working in the different parts of generalized symmetries. Recent developments in the mathematical structure and physical applications of generalized symmetries are discussed.

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 Systems Quantum Groups and Quantum Field Theories written by Alberto Ibort and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 508 pages. 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.

Download or read book Integrability written by Alexander Mikhailov and published by Springer Science & Business Media. This book was released on 2008-11-25 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: The principal aim of the book is to give a comprehensive account of the variety of approaches to such an important and complex concept as Integrability. Dev- oping mathematical models, physicists often raise the following questions: whether the model obtained is integrable or close in some sense to an integrable one and whether it can be studied in depth analytically. In this book we have tried to c- ate a mathematical framework to address these issues, and we give descriptions of methods and review results. In the Introduction we give a historical account of the birth and development of the theory of integrable equations, focusing on the main issue of the book – the concept of integrability itself. A universal de nition of Integrability is proving to be elusive despite more than 40 years of its development. Often such notions as “- act solvability” or “regular behaviour” of solutions are associated with integrable systems. Unfortunately these notions do not lead to any rigorous mathematical d- inition. A constructive approach could be based upon the study of hidden and rich algebraic or analytic structures associated with integrable equations. The requi- ment of existence of elements of these structures could, in principle, be taken as a de nition for integrability. It is astonishing that the nal result is not sensitive to the choice of the structure taken; eventually we arrive at the same pattern of eq- tions.