Download or read book Classical And Quantum Field Theory Of Exactly Soluble Nonlinear Systems written by Piotr Garbaczewski and published by World Scientific. This book was released on 1985-07-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents:Nonlinear Problems in 1 + 1 and Their LinearizationClassical Field Theory ModelsHamiltonian Formulation, Action-Angle Variables, Solitons, Classical Lattice Models and Lattice Approximants of Classical FieldsQuantization on a Lattice: Relationship Classical-QuantumQuantization on a Lattice: Simple Bose ModelsSpin 1/2 Lattice Systems Related to Nonlinear Bose Problems: Lattice FermionsQuantization in Continuum: Joint Bose-Fermi Spectral Problems in 1 + 1Quantum Meaning of Classical Field Theory for Fermi SystemsOn Infinite Constituent “Elementary” Systems: Canonical (Constituent) Quantization of Soliton FieldsTowards 1 + 3: Problems and Prospects Readership: Mathematical physicists and physicists. Keywords:Nonlinear Fields;Integrability;Solvable Models;Solitons;Continuum and Lattice Models;Quantization;Fermi Fields And Their Classical Counterparts;Relationship Classical-Quantum;Boson-Fermion Reciprocity (Bosonization)
Download or read book Classical and Quantum Field Theory of Exactly Soluble Nonlinear Systems written by P. Garbaczewski and published by World Scientific Publishing Company Incorporated. This book was released on 1985-01-01 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book On Klauder s Path written by Grard G. Emch and published by World Scientific. This book was released on 1994 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains contributions by friends, colleagues and associates of John R Klauder on the occasion of his 60th birthday.Klauder's scientific work embraces vast territories from quantum theories to general relativity, optics and chaotic dynamics. A recurrent theme in his research is the role played by coherent states, in particular, in connection with path integral formulations of quantization. Perhaps at a less lofty level, this concept has had at least two spectacular applications: as a powerful investigative tool in quantum optics and as a precursor to wavelets. In a different vein, Klauder also attacked specific, non-renormalizable but exactly soluble, hard-core models in field theory, where he uncovered what has since been called the Klauder phenomenon.The contributors to this volume represent the special brand of mathematicians and physicists John Klauder helped define throughout his seminal career in the industrial and academic worlds.
Download or read book Quantum Field Theory Perspective and Prospective written by Cécile Dewitt-Morette and published by Springer Science & Business Media. This book was released on 1999-03-31 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: Proceedings of the NATO Advanced Study Institute, Les Houches, France, 15-26 June 1998
Download or read book Non Linear Equations in Classical and Quantum Field Theory written by Norma Sanchez and published by Springer. This book was released on 2014-03-12 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Quantum Groups written by Heinz-Dietrich Doebner and published by Springer. This book was released on 2014-04-17 with total page 438 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough analysis of exactly soluble models in nonlinear classical systems and in quantum systems as well as recent studies in conformal quantum field theory have revealed the structure of quantum groups to be an interesting and rich framework for mathematical and physical problems. In this book, for the first time, authors from different schools review in an intelligible way the various competing approaches: inverse scattering methods, 2-dimensional statistical models, Yang-Baxter algebras, the Bethe ansatz, conformal quantum field theory, representations, braid group statistics, noncommutative geometry, and harmonic analysis.
Download or read book Quantum Groups written by Heinz Dietrich Doebner and published by Springer. This book was released on 1990 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: A thorough analysis of exactly soluble models in nonlinear classical systems and in quantum systems as well as recent studies in conformal quantum field theory have revealed the structure of quantum groups to be an interesting and rich framework for mathematical and physical problems. In this book, for the first time, authors from different schools review in an intelligible way the various competing approaches: inverse scattering methods, 2-dimensional statistical models, Yang-Baxter algebras, the Bethe ansatz, conformal quantum field theory, representations, braid group statistics, noncommutative geometry, and harmonic analysis.
Download or read book Nonlinear Dynamics and Quantum Chaos written by Sandro Wimberger and published by Springer Nature. This book was released on 2023-01-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a clear and concise introduction to the field of nonlinear dynamics and chaos, suitable for graduate students in mathematics, physics, chemistry, engineering, and in natural sciences in general. This second edition includes additional material and in particular a new chapter on dissipative nonlinear systems. The book provides a thorough and modern introduction to the concepts of dynamical systems' theory combining in a comprehensive way classical and quantum mechanical description. It is based on lectures on classical and quantum chaos held by the author at Heidelberg and Parma University. The book contains exercises and worked examples, which make it ideal for an introductory course for students as well as for researchers starting to work in the field.
Download or read book Classical and Quantum Nonlinear Integrable Systems written by A Kundu and published by CRC Press. This book was released on 2019-04-23 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Download or read book Classical Nonintegrability Quantum Chaos written by Andreas Knauf and published by Birkhäuser. This book was released on 2012-12-06 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our DMV Seminar on 'Classical Nonintegrability, Quantum Chaos' intended to introduce students and beginning researchers to the techniques applied in nonin tegrable classical and quantum dynamics. Several of these lectures are collected in this volume. The basic phenomenon of nonlinear dynamics is mixing in phase space, lead ing to a positive dynamical entropy and a loss of information about the initial state. The nonlinear motion in phase space gives rise to a linear action on phase space functions which in the case of iterated maps is given by a so-called transfer operator. Good mixing rates lead to a spectral gap for this operator. Similar to the use made of the Riemann zeta function in the investigation of the prime numbers, dynamical zeta functions are now being applied in nonlinear dynamics. In Chapter 2 V. Baladi first introduces dynamical zeta functions and transfer operators, illustrating and motivating these notions with a simple one-dimensional dynamical system. Then she presents a commented list of useful references, helping the newcomer to enter smoothly into this fast-developing field of research. Chapter 3 on irregular scattering and Chapter 4 on quantum chaos by A. Knauf deal with solutions of the Hamilton and the Schr6dinger equation. Scatter ing by a potential force tends to be irregular if three or more scattering centres are present, and a typical phenomenon is the occurrence of a Cantor set of bounded orbits. The presence of this set influences those scattering orbits which come close.
Download or read book Integrable Structures of Exactly Solvable Two Dimensional Models of Quantum Field Theory written by S. Pakuliak and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 334 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integrable quantum field theories and integrable lattice models have been studied for several decades, but during the last few years new ideas have emerged that have considerably changed the topic. The first group of papers published here is concerned with integrable structures of quantum lattice models related to quantum group symmetries. The second group deals with the description of integrable structures in two-dimensional quantum field theories, especially boundary problems, thermodynamic Bethe ansatz and form factor problems. Finally, a major group of papers is concerned with the purely mathematical framework that underlies the physically-motivated research on quantum integrable models, including elliptic deformations of groups, representation theory of non-compact quantum groups, and quantization of moduli spaces.
Download or read book Classical and Quantum Physics written by G. Marmo and published by Springer Nature. This book was released on 2019-10-26 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings is based on the interdisciplinary workshop held in Madrid, 5-9 March 2018, dedicated to Alberto Ibort on his 60th birthday. Alberto has great and significantly contributed to many fields of mathematics and physics, always with highly original and innovative ideas.Most of Albertos’s scientific activity has been motivated by geometric ideas, concepts and tools that are deeply related to the framework of classical dynamics and quantum mechanics.Let us mention some of the fields of expertise of Alberto Ibort:Geometric Mechanics; Constrained Systems; Variational Principles; Multisymplectic structures for field theories; Super manifolds; Inverse problem for Bosonic and Fermionic systems; Quantum Groups, Integrable systems, BRST Symmetries; Implicit differential equations; Yang-Mills Theories; BiHamiltonian Systems; Topology Change and Quantum Boundary Conditions; Classical and Quantum Control; Orthogonal Polynomials; Quantum Field Theory and Noncommutative Spaces; Classical and Quantum Tomography; Quantum Mechanics on phase space; Wigner-Weyl formalism; Lie-Jordan Algebras, Classical and Quantum; Quantum-to-Classical transition; Contraction of Associative Algebras; contact geometry, among many others.In each contribution, one may find not only technical novelties but also completely new way of looking at the considered problems. Even an experienced reader, reading Alberto's contributions on his field of expertise, will find new perspectives on the considered topic.His enthusiasm is happily contagious, for this reason he has had, and still has, very bright students wishing to elaborate their PhD thesis under his guidance.What is more impressive, is the broad list of rather different topics on which he has contributed.
Download or read book Quantum Non linear Sigma Models written by Sergei V. Ketov and published by Springer Science & Business Media. This book was released on 2000-09-14 with total page 436 pages. Available in PDF, EPUB and Kindle. Book excerpt: Offers a systematic presentation of the modern quantum field theory of non-linear sigma-models. These models are very popular in theoretical high energy physics, string theory, and statistical physics. The geometric and quantum renormalization properties of the most general non-linear sigma-models are considered in detail within the framework of quantum perturbation theory. The main applications to be considered in the book can be found in string theory, conformal field theory, and general relativity.
Download or read book Quantum Mechanics in Nonlinear Systems written by Xiao-Feng Pang and published by World Scientific. This book was released on 2005 with total page 646 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the history of physics and science, quantum mechanics has served as the foundation of modern science. This book discusses the properties of microscopic particles in nonlinear systems, principles of the nonlinear quantum mechanical theory, and its applications in condensed matter, polymers and biological systems.The book is essentially composed of three parts. The first part presents a review of linear quantum mechanics, as well as theoretical and experimental fundamentals that establish the nonlinear quantum mechanical theory. The theory itself and its essential features are covered in the second part. In the final part, extensive applications of this theory in physics, biology and polymer are introduced. The whole volume forms a complete system of nonlinear quantum mechanics.The book is intended for researchers, graduate students as well as upper-level undergraduates.
Download or read book Quantum Field Theory I Basics in Mathematics and Physics written by Eberhard Zeidler and published by Springer Science & Business Media. This book was released on 2007-04-18 with total page 1060 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first volume of a modern introduction to quantum field theory which addresses both mathematicians and physicists, at levels ranging from advanced undergraduate students to professional scientists. The book bridges the acknowledged gap between the different languages used by mathematicians and physicists. For students of mathematics the author shows that detailed knowledge of the physical background helps to motivate the mathematical subjects and to discover interesting interrelationships between quite different mathematical topics. For students of physics, fairly advanced mathematics is presented, which goes beyond the usual curriculum in physics.
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.
