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.

Download or read book Ludwig Faddeev Memorial Volume A Life In Mathematical Physics written by Mo-lin Ge and published by World Scientific. This book was released on 2018-05-21 with total page 634 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ludwig Faddeev is widely recognized as one of the titans of 20th century mathematical physics. His fundamental contributions to scattering theory, quantum gauge theories, and the theory of classical and quantum completely integrable systems played a key role in shaping modern mathematical physics.Ludwig Faddeev's major achievements include the solution of the three-body problem in quantum mechanics, the mathematical formulation of quantum gauge theories and corresponding Feynman rules, Hamiltonian and algebraic methods in mathematical physics, with applications to gauge theories with anomalies, quantum systems with constraints and solitons, the discovery of the algebraic structure of classical and quantum integrable systems and quantum groups, and solitons with the topology of knots.Faddeev's name is imprinted in many areas of mathematics and theoretical physics, including 'Faddeev's equations' and 'Faddeev's Green function' in scattering theory, 'Faddeev-Popov ghosts' and 'Faddeev-Popov determinant' in gauge theories, 'Gardner-Faddeev-Zakharov bracket' for the KdV equation, 'Faddeev-Zamolodchikov algebra' in quantum integrable systems, 'Faddeev-Reshetikhin-Takhtajan construction' in the theory of quantum groups, knotted solitons in the 'Skyrme-Faddeev model' and many others.Ludwig Faddeev founded the St. Petersburg school of modern mathematical physics and distinguished himself by serving the mathematics community for over three decades including his leadership of the International Mathematical Union in the period of 1986-1990. He was conferred numerous prizes and memberships of prestigious institutions in recognition of the importance of his work. These include the Dannie Heineman Prize for Mathematical Physics, the Dirac Medal, the Max Planck Medal, the Shaw Prize and the Lomonosov Gold Medal among others.A gathering of contributions from some of the biggest names in mathematics and physics, this volume serves as a tribute to this legendary figure. Volume contributors include: Fields medalist Sir Michael Atiyah, Jürg Fröhlich, Roman Jackiw, Vladimir Korepin, Nikita Nekrasov, André Neveu, Alexander M Polyakov, Samson Shatashvili, Fedor Smirnov as well as Nobel laureates Frank Wilczek and C N Yang.

Download or read book An Introduction to Integrable Techniques for One Dimensional Quantum Systems written by Fabio Franchini and published by Springer. This book was released on 2017-05-25 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the reader to basic notions of integrable techniques for one-dimensional quantum systems. In a pedagogical way, a few examples of exactly solvable models are worked out to go from the coordinate approach to the Algebraic Bethe Ansatz, with some discussion on the finite temperature thermodynamics. The aim is to provide the instruments to approach more advanced books or to allow for a critical reading of research articles and the extraction of useful information from them. We describe the solution of the anisotropic XY spin chain; of the Lieb-Liniger model of bosons with contact interaction at zero and finite temperature; and of the XXZ spin chain, first in the coordinate and then in the algebraic approach. To establish the connection between the latter and the solution of two dimensional classical models, we also introduce and solve the 6-vertex model. Finally, the low energy physics of these integrable models is mapped into the corresponding conformal field theory. Through its style and the choice of topics, this book tries to touch all fundamental ideas behind integrability and is meant for students and researchers interested either in an introduction to later delve in the advance aspects of Bethe Ansatz or in an overview of the topic for broadening their culture.

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.

Download or read book Quantum Groups Integrable Models And Statistiacal Systems written by Jean Letourneux and published by World Scientific. This book was released on 1993-12-22 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the lectures presented at the workshop on “Quantum Groups, Integrable Models and Statistical Systems”. The papers give either a full exposition of original results or a review of fundamental aspects of this most active research area.

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 Future Directions of Nonlinear Dynamics in Physical and Biological Systems written by P.L. Christiansen and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 549 pages. Available in PDF, EPUB and Kindle. Book excerpt: Early in 1990 a scientific committee was formed for the purpose of organizing a high-level scientific meeting on Future Directions of Nonlinear Dynamics in Physical and Biological Systems, in honor of Alwyn Scott's 60th birthday (December 25, 1991). As preparations for the meeting proceeded, they were met with an unusually broad-scale and high level of enthusiasm on the part of the international nonlinear science community, resulting in a participation by 168 scientists from 23 different countries in the conference, which was held July 23 to August 11992 at the Laboratory of Applied Mathematical Physics and the Center for Modelling, Nonlinear Dynamics and Irreversible Thermodynamics (MIDIT) of the Technical University of Denmark. During the meeting about 50 lectures and 100 posters were presented in 9 working days. The contributions to this present volume have been grouped into the following chapters: 1. Integrability, Solitons, and Coherent Structures 2. Nonlinear Evolution Equations and Diffusive Systems 3. Chaotic and Stochastic Dynamics 4. Classical and Quantum Lattices and Fields 5. Superconductivity and Superconducting Devices 6. Nonlinear Optics 7. Davydov Solitons and Biomolecular Dynamics 8. Biological Systems and Neurophysics. AI Scott has made early and fundamental contributions to many of these different areas of nonlinear science. They form an important subset of the total number of the papers and posters presented at the meeting. Other papers from the meeting are being published in a special issue of Physica D Nonlinear Phenomena.

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 Noncommutative Spacetimes written by Paolo Aschieri and published by Springer Science & Business Media. This book was released on 2009-07-14 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: There are many approaches to noncommutative geometry and to its use in physics. This volume addresses the subject by combining the deformation quantization approach, based on the notion of star-product, and the deformed quantum symmetries methods, based on the theory of quantum groups. The aim of this work is to give an introduction to this topic and to prepare the reader to enter the research field quickly. The order of the chapters is "physics first": the mathematics follows from the physical motivations (e.g. gauge field theories) in order to strengthen the physical intuition. The new mathematical tools, in turn, are used to explore further physical insights. A last chapter has been added to briefly trace Julius Wess' (1934-2007) seminal work in the field.

Download or read book Nonlinearity Integrability And All That Twenty Years After Needs 79 Proceedings Of The Workshop written by M Boiti and published by World Scientific. This book was released on 2000-05-12 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses achievements in the last 20 years, recent developments and future perspectives in nonlinear science. Both continuous and discrete systems — classical and quantum — are considered.

Download or read book Calogero Moser Sutherland Models written by Jan F. van Diejen and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the 1970s F. Calogero and D. Sutherland discovered that for certain potentials in one-dimensional systems, but for any number of particles, the Schrödinger eigenvalue problem is exactly solvable. Until then, there was only one known nontrivial example of an exactly solvable quantum multi-particle problem. J. Moser subsequently showed that the classical counterparts to these models is also amenable to an exact analytical approach. The last decade has witnessed a true explosion of activities involving Calogero-Moser-Sutherland models, and these now play a role in research areas ranging from theoretical physics (such as soliton theory, quantum field theory, string theory, solvable models of statistical mechanics, condensed matter physics, and quantum chaos) to pure mathematics (such as representation theory, harmonic analysis, theory of special functions, combinatorics of symmetric functions, dynamical systems, random matrix theory, and complex geometry). The aim of this volume is to provide an overview of the many branches into which research on CMS systems has diversified in recent years. The contributions are by leading researchers from various disciplines in whose work CMS systems appear, either as the topic of investigation itself or as a tool for further applications.

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 Spinning Strings and Correlation Functions in the AdS CFT Correspondence written by Juan Miguel Nieto and published by Springer. This book was released on 2018-07-21 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book addresses several aspects of the integrable structure of the AdS/CFT correspondence. In particular it presents computations made on both sides of the AdS/CFT correspondence, at weak and at strong coupling. On the string theory side of the correspondence, the book focuses on the evaluation of the energy spectrum of closed string solutions moving in some deformed backgrounds that preserve integrability. On the gauge theory side, it explores various formal problems arising in the computation of two and three-point functions by means of the Algebraic Bethe Ansatz and the Quantum Inverse Scattering method. The book features numerous results on integrability in the context of the AdS/CFT correspondence. Self-contained and pedagogical, it includes general discussions and detailed presentations on the use of integrable systems techniques and their applications.

Download or read book Quantum Inverse Scattering Method and Correlation Functions written by V. E. Korepin and published by Cambridge University Press. This book was released on 1997-03-06 with total page 582 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantum inverse scattering method is a means of finding exact solutions of two-dimensional models in quantum field theory and statistical physics (such as the sine-Go rdon equation or the quantum non-linear Schrödinger equation). These models are the subject of much attention amongst physicists and mathematicians.The present work is an introduction to this important and exciting area. It consists of four parts. The first deals with the Bethe ansatz and calculation of physical quantities. The authors then tackle the theory of the quantum inverse scattering method before applying it in the second half of the book to the calculation of correlation functions. This is one of the most important applications of the method and the authors have made significant contributions to the area. Here they describe some of the most recent and general approaches and include some new results.The book will be essential reading for all mathematical physicists working in field theory and statistical physics.

Download or read book Nonlinear Mathematical Physics and Natural Hazards written by Boyka Aneva and published by Springer. This book was released on 2015-02-12 with total page 157 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to current advances in the field of nonlinear mathematical physics and modeling of critical phenomena that can lead to catastrophic events. Pursuing a multidisciplinary approach, it gathers the work of scientists who are developing mathematical and computational methods for the study and analysis of nonlinear phenomena and who are working actively to apply these tools and create conditions to mitigate and reduce the negative consequences of natural and socio-economic disaster risk. This book summarizes the contributions of the International School and Workshop on Nonlinear Mathematical Physics and Natural Hazards, organized within the framework of the South East Europe Network in Mathematical and Theoretical Physics (SEENET MTP) and supported by UNESCO. It was held at the Bulgarian Academy of Sciences from November 28 to December 2, 2013. The contributions are divided into two major parts in keeping with the scientific program of the meeting. Among the topics covered in Part I (Nonlinear Mathematical Physics towards Critical Phenomena) are predictions and correlations in self organized criticality, space-time structure of extreme current and activity events in exclusion processes, quantum spin chains and integrability of many-body systems, applications of discriminantly separable polynomials, MKdV-type equations, and chaotic behavior in Yang-Mills theories. Part II (Seismic Hazard and Risk) is devoted to probabilistic seismic hazard assessment, seismic risk mapping, seismic monitoring, networking and data processing in Europe, mainly in South-East Europe. The book aims to promote collaboration at the regional and European level to better understand and model phenomena that can cause natural and socio-economic disasters, and to contribute to the joint efforts to mitigate the negative consequence of natural disasters. This collection of papers reflects contemporary efforts on capacity building through developing skills, exchanging knowledge and practicing mathematical methods for modeling nonlinear phenomena, disaster risk preparedness and natural hazards mitigation. The target audience includes students and researchers in mathematical and theoretical physics, earth physics, applied physics, geophysics, seismology and earthquake danger and risk mitigation.

Download or read book New Trends in Quantum Integrable Systems 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 is exposed to the most recent developments in the field of quantum integrable systems and related areas of mathematical physics.

Download or read book String Math 2013 written by Ron Donagi, Michael R. Douglas and published by American Mathematical Soc.. This book was released on 2014-12-02 with total page 386 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of the conference `String-Math 2013' which was held June 17-21, 2013 at the Simons Center for Geometry and Physics at Stony Brook University. This was the third in a series of annual meetings devoted to the interface of mathematics and string theory. Topics include the latest developments in supersymmetric and topological field theory, localization techniques, the mathematics of quantum field theory, superstring compactification and duality, scattering amplitudes and their relation to Hodge theory, mirror symmetry and two-dimensional conformal field theory, and many more. This book will be important reading for researchers and students in the area, and for all mathematicians and string theorists who want to update themselves on developments in the math-string interface.