Elements Of Classical And Quantum Integrable Systems PDF Download
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Author | : Gleb Arutyunov |
Publisher | : Springer |
Total Pages | : 414 |
Release | : 2019-07-23 |
Genre | : Science |
ISBN | : 303024198X |
Download Elements of Classical and Quantum Integrable Systems Book in PDF, ePub and Kindle
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.
Author | : A Kundu |
Publisher | : CRC Press |
Total Pages | : 320 |
Release | : 2019-04-23 |
Genre | : Science |
ISBN | : 9781420034615 |
Download Classical and Quantum Nonlinear Integrable Systems Book in PDF, ePub and Kindle
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 | : Asesh Roy Chowdhury |
Publisher | : CRC Press |
Total Pages | : 425 |
Release | : 2004-01-28 |
Genre | : Science |
ISBN | : 0203498011 |
Download Quantum Integrable Systems Book in PDF, ePub and Kindle
The study of integrable systems has opened new horizons in classical physics over the past few decades, particularly in the subatomic world. Yet despite the field now having reached a level of maturity, very few books provide an introduction to the field accessible to specialists and nonspecialists alike, and none offer a systematic survey of the m
Author | : Mauro Carfora |
Publisher | : World Scientific |
Total Pages | : 194 |
Release | : 1992-04-30 |
Genre | : |
ISBN | : 9814554766 |
Download Integrable Systems And Quantum Groups Book in PDF, ePub and Kindle
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 | : Alberto Ibort |
Publisher | : Springer Science & Business Media |
Total Pages | : 508 |
Release | : 2012-12-06 |
Genre | : Science |
ISBN | : 9401119805 |
Download Integrable Systems, Quantum Groups, and Quantum Field Theories Book in PDF, ePub and Kindle
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 | : Maciej Błaszak |
Publisher | : Springer |
Total Pages | : 460 |
Release | : 2019-06-11 |
Genre | : Science |
ISBN | : 3030183793 |
Download Quantum versus Classical Mechanics and Integrability Problems Book in PDF, ePub and Kindle
This accessible monograph introduces physicists to the general relation between classical and quantum mechanics based on the mathematical idea of deformation quantization and describes an original approach to the theory of quantum integrable systems developed by the author.The first goal of the book is to develop of a common, coordinate free formulation of classical and quantum Hamiltonian mechanics, framed in common mathematical language.In particular, a coordinate free model of quantum Hamiltonian systems in Riemannian spaces is formulated, based on the mathematical idea of deformation quantization, as a complete physical theory with an appropriate mathematical accuracy.The second goal is to develop of a theory which allows for a deeper understanding of classical and quantum integrability. For this reason the modern separability theory on both classical and quantum level is presented. In particular, the book presents a modern geometric separability theory, based on bi-Poissonian and bi-presymplectic representations of finite dimensional Liouville integrable systems and their admissible separable quantizations.The book contains also a generalized theory of classical Stäckel transforms and the discussion of the concept of quantum trajectories.In order to make the text consistent and self-contained, the book starts with a compact overview of mathematical tools necessary for understanding the remaining part of the book. However, because the book is dedicated mainly to physicists, despite its mathematical nature, it refrains from highlighting definitions, theorems or lemmas.Nevertheless, all statements presented are either proved or the reader is referred to the literature where the proof is available.
Author | : John P. Harnad |
Publisher | : American Mathematical Soc. |
Total Pages | : 282 |
Release | : 2000 |
Genre | : Mathematics |
ISBN | : 0821820931 |
Download Integrable Systems: From Classical to Quantum Book in PDF, ePub and Kindle
This volume presents the papers based upon lectures given at the 1999 Séminaire de Mathémathiques Supérieurs held in Montreal. It includes contributions from many of the most active researchers in the field. This subject has been in a remarkably active state of development throughout the past three decades, resulting in new motivation for study in r s3risingly different directions. Beyond the intrinsic interest in the study of integrable models of many-particle systems, spin chains, lattice and field theory models at both the classical and the quantum level, and completely solvable models in statistical mechanics, there have been new applications in relation to a number of other fields of current interest. These fields include theoretical physics and pure mathematics, for example the Seiberg-Witten approach to supersymmetric Yang-Mills theory, the spectral theory of random matrices, topological models of quantum gravity, conformal field theory, mirror symmetry, quantum cohomology, etc. This collection gives a nice cross-section of the current state of the work in the area of integrable systems which is presented by some of the leading active researchers in this field. The scope and quality of the articles in this volume make this a valuable resource for those interested in an up-to-date introduction and an overview of many of the main areas of study in the theory of integral systems.
Author | : A Kundu |
Publisher | : CRC Press |
Total Pages | : 166 |
Release | : 2019-04-23 |
Genre | : Science |
ISBN | : 0429525044 |
Download Classical and Quantum Nonlinear Integrable Systems Book in PDF, ePub and Kindle
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 | : Mo-lin Ge |
Publisher | : World Scientific |
Total Pages | : 242 |
Release | : 1992-05-30 |
Genre | : |
ISBN | : 9814555835 |
Download Quantum Group And Quantum Integrable Systems - Nankai Lectures On Mathematical Physics Book in PDF, ePub and Kindle
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 | : Ahmed Lesfari |
Publisher | : John Wiley & Sons |
Total Pages | : 340 |
Release | : 2022-07-13 |
Genre | : Mathematics |
ISBN | : 1786308274 |
Download Integrable Systems Book in PDF, ePub and Kindle
This book illustrates the powerful interplay between topological, algebraic and complex analytical methods, within the field of integrable systems, by addressing several theoretical and practical aspects. Contemporary integrability results, discovered in the last few decades, are used within different areas of mathematics and physics. Integrable Systems incorporates numerous concrete examples and exercises, and covers a wealth of essential material, using a concise yet instructive approach. This book is intended for a broad audience, ranging from mathematicians and physicists to students pursuing graduate, Masters or further degrees in mathematics and mathematical physics. It also serves as an excellent guide to more advanced and detailed reading in this fundamental area of both classical and contemporary mathematics.