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Integrability Quantization And Geometry I Integrable Systems
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Book Synopsis Integrability, Quantization, and Geometry: I. Integrable Systems by : Sergey Novikov
Download or read book Integrability, Quantization, and Geometry: I. Integrable Systems written by Sergey Novikov and published by American Mathematical Soc.. This book was released on 2021-04-12 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Book Synopsis Integrability, Quantization, and Geometry by : Sergeĭ Petrovich Novikov
Download or read book Integrability, Quantization, and Geometry written by Sergeĭ Petrovich Novikov and published by . This book was released on 2021 with total page 542 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles written in memory of Boris Dubrovin (1950-2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher.The contributions to this collection of papers are split into two parts: ""Integrable Systems"" and ""Quantum Theories and Algebraic Geometry"", reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, i.
Book Synopsis Elements of Classical and Quantum Integrable Systems by : Gleb Arutyunov
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.
Book Synopsis Geometric and Quantum Aspects of Integrable Systems by : G. F. Helminck
Download or read book Geometric and Quantum Aspects of Integrable Systems written by G. F. Helminck and published by . This book was released on 2014-01-15 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integrable Systems: From Classical to Quantum by : John P. Harnad
Download or read book Integrable Systems: From Classical to Quantum written by John P. Harnad and published by American Mathematical Soc.. This book was released on 2000 with total page 282 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
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 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.
Book Synopsis Geometric and Quantum Aspects of Integrable Systems by : G. F. Helminck
Download or read book Geometric and Quantum Aspects of Integrable Systems written by G. F. Helminck and published by . This book was released on 1993 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Geometric and Quantum Aspects of Integrable Systems by : G.F. Helminck
Download or read book Geometric and Quantum Aspects of Integrable Systems written by G.F. Helminck and published by Springer. This book was released on 1993-11-30 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a collection of outstanding review papers on integrable systems. It gives the algebraic geometric aspects of the subject, describes integrability techniques e.g. for the modified KdV equation, integrability of Hamiltonian systems, hierarchies of equations, probability distribution of eigenvalues, and modern aspects of quantum groups. It addresses researchers in mathematics and mathematical physics.
Book Synopsis New Trends In Quantum Integrable Systems - Proceedings Of The Infinite Analysis 09 by : Boris Feigin
Download or read book New Trends In Quantum Integrable Systems - Proceedings Of The Infinite Analysis 09 written by Boris Feigin and published by World Scientific. This book was released on 2010-10-29 with total page 517 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is the result of the international workshop on New Trends in Quantum Integrable Systems that was held in Kyoto, Japan, from 27 to 31 July 2009. As a continuation of the RIMS Research Project “Method of Algebraic Analysis in Integrable Systems” in 2004, the workshop's aim was to cover exciting new developments that have emerged during the recent years.Collected here are research articles based on the talks presented at the workshop, including the latest results obtained thereafter. The subjects discussed range across diverse areas such as correlation functions of solvable models, integrable models in quantum field theory, conformal field theory, mathematical aspects of Bethe ansatz, special functions and integrable differential/difference equations, representation theory of infinite dimensional algebras, integrable models and combinatorics.Through these topics, the reader can learn about the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.
Book Synopsis Quantum Theory, Deformation and Integrability by : R. Carroll
Download or read book Quantum Theory, Deformation and Integrability written by R. Carroll and published by Elsevier. This book was released on 2000-11-09 with total page 421 pages. Available in PDF, EPUB and Kindle. Book excerpt: About four years ago a prominent string theorist was quoted as saying that it might be possible to understand quantum mechanics by the year 2000. Sometimes new mathematical developments make such understanding appear possible and even close, but on the other hand, increasing lack of experimental verification make it seem to be further distant. In any event one seems to arrive at new revolutions in physics and mathematics every year. This book hopes to convey some of the excitment of this period, but will adopt a relatively pedestrian approach designed to illuminate the relations between quantum and classical. There will be some discussion of philosophical matters such as measurement, uncertainty, decoherence, etc. but philosophy will not be emphasized; generally we want to enjoy the fruits of computation based on the operator formulation of QM and quantum field theory. In Chapter 1 connections of QM to deterministic behavior are exhibited in the trajectory representations of Faraggi-Matone. Chapter 1 also includes a review of KP theory and some preliminary remarks on coherent states, density matrices, etc. and more on deterministic theory. We develop in Chapter 4 relations between quantization and integrability based on Moyal brackets, discretizations, KP, strings and Hirota formulas, and in Chapter 2 we study the QM of embedded curves and surfaces illustrating some QM effects of geometry. Chapter 3 is on quantum integrable systems, quantum groups, and modern deformation quantization. Chapter 5 involves the Whitham equations in various roles mediating between QM and classical behavior. In particular, connections to Seiberg-Witten theory (arising in N = 2 supersymmetric (susy) Yang-Mills (YM) theory) are discussed and we would still like to understand more deeply what is going on. Thus in Chapter 5 we will try to give some conceptual background for susy, gauge theories, renormalization, etc. from both a physical and mathematical point of view. In Chapter 6 we continue the deformation quantization then by exhibiting material based on and related to noncommutative geometry and gauge theory.
Book Synopsis Integrability, Quantization, and Geometry by : Sergej P. Novikov
Download or read book Integrability, Quantization, and Geometry written by Sergej P. Novikov and published by . This book was released on 2021 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Volume 1. Integrable systems -- Volume 2. Quantum theories and algebraic geometry.
Book Synopsis Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry by : Sergey Novikov
Download or read book Integrability, Quantization, and Geometry: II. Quantum Theories and Algebraic Geometry written by Sergey Novikov and published by American Mathematical Soc.. This book was released on 2021-04-12 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a collection of articles written in memory of Boris Dubrovin (1950–2019). The authors express their admiration for his remarkable personality and for the contributions he made to mathematical physics. For many of the authors, Dubrovin was a friend, colleague, inspiring mentor, and teacher. The contributions to this collection of papers are split into two parts: “Integrable Systems” and “Quantum Theories and Algebraic Geometry”, reflecting the areas of main scientific interests of Dubrovin. Chronologically, these interests may be divided into several parts: integrable systems, integrable systems of hydrodynamic type, WDVV equations (Frobenius manifolds), isomonodromy equations (flat connections), and quantum cohomology. The articles included in the first part are more or less directly devoted to these areas (primarily with the first three listed above). The second part contains articles on quantum theories and algebraic geometry and is less directly connected with Dubrovin's early interests.
Book Synopsis Symplectic Geometry, Groupoids, and Integrable Systems by : Pierre Dazord
Download or read book Symplectic Geometry, Groupoids, and Integrable Systems written by Pierre Dazord and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 318 pages. Available in PDF, EPUB and Kindle. Book excerpt: The papers, some of which are in English, the rest in French, in this volume are based on lectures given during the meeting of the Seminare Sud Rhodanien de Geometrie (SSRG) organized at the Mathematical Sciences Research Institute in 1989. The SSRG was established in 1982 by geometers and mathematical physicists with the aim of developing and coordinating research in symplectic geometry and its applications to analysis and mathematical physics. Among the subjects discussed at the meeting, a special role was given to the theory of symplectic groupoids, the subject of fruitful collaboration involving geometers from Berkeley, Lyon, and Montpellier.
Book Synopsis Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds by : A.K. Prykarpatsky
Download or read book Algebraic Integrability of Nonlinear Dynamical Systems on Manifolds written by A.K. Prykarpatsky and published by Springer Science & Business Media. This book was released on 2013-04-09 with total page 555 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent times it has been stated that many dynamical systems of classical mathematical physics and mechanics are endowed with symplectic structures, given in the majority of cases by Poisson brackets. Very often such Poisson structures on corresponding manifolds are canonical, which gives rise to the possibility of producing their hidden group theoretical essence for many completely integrable dynamical systems. It is a well understood fact that great part of comprehensive integrability theories of nonlinear dynamical systems on manifolds is based on Lie-algebraic ideas, by means of which, in particular, the classification of such compatibly bi Hamiltonian and isospectrally Lax type integrable systems has been carried out. Many chapters of this book are devoted to their description, but to our regret so far the work has not been completed. Hereby our main goal in each analysed case consists in separating the basic algebraic essence responsible for the complete integrability, and which is, at the same time, in some sense universal, i. e. , characteristic for all of them. Integrability analysis in the framework of a gradient-holonomic algorithm, devised in this book, is fulfilled through three stages: 1) finding a symplectic structure (Poisson bracket) transforming an original dynamical system into a Hamiltonian form; 2) finding first integrals (action variables or conservation laws); 3) defining an additional set of variables and some functional operator quantities with completely controlled evolutions (for instance, as Lax type representation).
Book Synopsis What Is Integrability? by : Vladimir E. Zakharov
Download or read book What Is Integrability? written by Vladimir E. Zakharov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: The idea of devoting a complete book to this topic was born at one of the Workshops on Nonlinear and Turbulent Processes in Physics taking place reg ularly in Kiev. With the exception of E. D. Siggia and N. Ercolani, all authors of this volume were participants at the third of these workshops. All of them were acquainted with each other and with each other's work. Yet it seemed to be somewhat of a discovery that all of them were and are trying to understand the same problem - the problem of integrability of dynamical systems, primarily Hamiltonian ones with an infinite number of degrees of freedom. No doubt that they (or to be more exact, we) were led to this by the logical process of scientific evolution which often leads to independent, almost simultaneous discoveries. Integrable, or, more accurately, exactly solvable equations are essential to theoretical and mathematical physics. One could say that they constitute the "mathematical nucleus" of theoretical physics whose goal is to describe real clas sical or quantum systems. For example, the kinetic gas theory may be considered to be a theory of a system which is trivially integrable: the system of classical noninteracting particles. One of the main tasks of quantum electrodynamics is the development of a theory of an integrable perturbed quantum system, namely, noninteracting electromagnetic and electron-positron fields.
Book Synopsis Quantization, Geometry and Noncommutative Structures in Mathematics and Physics by : Alexander Cardona
Download or read book Quantization, Geometry and Noncommutative Structures in Mathematics and Physics written by Alexander Cardona and published by Springer. This book was released on 2017-10-26 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents various ongoing approaches to the vast topic of quantization, which is the process of forming a quantum mechanical system starting from a classical one, and discusses their numerous fruitful interactions with mathematics.The opening chapter introduces the various forms of quantization and their interactions with each other and with mathematics.A first approach to quantization, called deformation quantization, consists of viewing the Planck constant as a small parameter. This approach provides a deformation of the structure of the algebra of classical observables rather than a radical change in the nature of the observables. When symmetries come into play, deformation quantization needs to be merged with group actions, which is presented in chapter 2, by Simone Gutt.The noncommutativity arising from quantization is the main concern of noncommutative geometry. Allowing for the presence of symmetries requires working with principal fiber bundles in a non-commutative setup, where Hopf algebras appear naturally. This is the topic of chapter 3, by Christian Kassel. Nichols algebras, a special type of Hopf algebras, are the subject of chapter 4, by Nicolás Andruskiewitsch. The purely algebraic approaches given in the previous chapters do not take the geometry of space-time into account. For this purpose a special treatment using a more geometric point of view is required. An approach to field quantization on curved space-time, with applications to cosmology, is presented in chapter 5 in an account of the lectures of Abhay Ashtekar that brings a complementary point of view to non-commutativity.An alternative quantization procedure is known under the name of string theory. In chapter 6 its supersymmetric version is presented. Superstrings have drawn the attention of many mathematicians, due to its various fruitful interactions with algebraic geometry, some of which are described here. The remaining chapters discuss further topics, as the Batalin-Vilkovisky formalism and direct products of spectral triples.This volume addresses both physicists and mathematicians and serves as an introduction to ongoing research in very active areas of mathematics and physics at the border line between geometry, topology, algebra and quantum field theory.
Book Synopsis Recent Developments in Integrable Systems and Related Topics of Mathematical Physics by : Victor M. Buchstaber
Download or read book Recent Developments in Integrable Systems and Related Topics of Mathematical Physics written by Victor M. Buchstaber and published by Springer. This book was released on 2018-12-30 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume, whose contributors include leading researchers in their field, covers a wide range of topics surrounding Integrable Systems, from theoretical developments to applications. Comprising a unique collection of research articles and surveys, the book aims to serve as a bridge between the various areas of Mathematics related to Integrable Systems and Mathematical Physics. Recommended for postgraduate students and early career researchers who aim to acquire knowledge in this area in preparation for further research, this book is also suitable for established researchers aiming to get up to speed with recent developments in the area, and may very well be used as a guide for further study.
