Classical And Quantum Field Theory Of Exactly Soluble Nonlinear Systems
Classical And Quantum Field Theory Of Exactly Soluble Nonlinear Systems

Author: Piotr Garbaczewski

Publisher: World Scientific

Published: 1985-07-01

Total Pages: 260

ISBN-13: 9814513571

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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)

On Klauder's Path
On Klauder's Path

Author: G‚rard G. Emch

Publisher: World Scientific

Published: 1994

Total Pages: 290

ISBN-13: 9789810216870

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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.

Quantum Field Theory I: Basics in Mathematics and Physics
Quantum Field Theory I: Basics in Mathematics and Physics

Author: Eberhard Zeidler

Publisher: Springer Science & Business Media

Published: 2007-04-18

Total Pages: 1060

ISBN-13: 354034764X

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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.

Quantum Mechanics in Nonlinear Systems
Quantum Mechanics in Nonlinear Systems

Author: Xiao-Feng Pang

Publisher: World Scientific

Published: 2005

Total Pages: 644

ISBN-13: 9812561161

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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.

Quantum Field Theory of Many-Body Systems
Quantum Field Theory of Many-Body Systems

Author: Xiao-Gang Wen

Publisher: OUP Oxford

Published: 2004-06-04

Total Pages: 520

ISBN-13: 0191523968

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For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been the emergence of a new paradigm associated with fractionalisation, topological order, emergent gauge bosons and fermions, and string condensation. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and fermions in the universe. This book is a pedagogical and systematic introduction to the new concepts and quantum field theoretical methods (which have fuelled the rapid developments) in condensed matter physics. It discusses many basic notions in theoretical physics which underlie physical phenomena in nature. Topics covered are dissipative quantum systems, boson condensation, symmetry breaking and gapless excitations, phase transitions, Fermi liquids, spin density wave states, Fermi and fractional statistics, quantum Hall effects, topological and quantum order, spin liquids, and string condensation. Methods covered are the path integral, Green's functions, mean-field theory, effective theory, renormalization group, bosonization in one- and higher dimensions, non-linear sigma-model, quantum gauge theory, dualities, slave-boson theory, and exactly soluble models beyond one-dimension. This book is aimed at teaching graduate students and bringing them to the frontiers of research in condensed matter physics.

Quantum Field Theory And Its Macroscopic Manifestations: Boson Condensation, Ordered Patterns And Topological Defects
Quantum Field Theory And Its Macroscopic Manifestations: Boson Condensation, Ordered Patterns And Topological Defects

Author: Massimo Blasone

Publisher: World Scientific

Published: 2011-02-21

Total Pages: 545

ISBN-13: 1908978686

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Quantum dynamics underlies macroscopic systems exhibiting some kind of ordering, such as superconductors, ferromagnets and crystals. Even large scale structures in the Universe and ordering in biological systems appear to be the manifestation of microscopic dynamics ruling their elementary components. The scope of this book is to answer questions such as: how it happens that the mesoscopic/macroscopic scale and stability characterizing those systems are dynamically generated out of the microscopic scale of fluctuating quantum components; how quantum particles coexist and interact with classically behaving macroscopic objects, e.g. vortices, magnetic domains and other topological defects. The quantum origin of topological defects and their interaction with quanta is a crucial issue for the understanding of symmetry breaking phase transitions and structure formation in a wide range of systems from condensed matter to cosmology. Deliberately not discussing other important problems, primarily renormalization problems, this book provides answers to such questions in a unitary, self-consistent physical and mathematical framework, which makes it unique in the panorama of existing texts on a similar subject. Crystals, ferromagnets and superconductors appear to be macroscopic quantum systems, i.e. their macroscopic properties cannot be explained without recourse to the underlying quantum dynamics. Recognizing that quantum field dynamics is not confined to the microscopic world is one of the achievements of this book, also marking its difference from other texts. The combined use of algebraic methods, and operator and functional formalism constitutes another distinctive, valuable feature./a

Coherent States
Coherent States

Author: John R. Klauder

Publisher: World Scientific

Published: 1985

Total Pages: 934

ISBN-13: 9789971966522

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This volume is a review on coherent states and some of their applications. The usefulness of the concept of coherent states is illustrated by considering specific examples from the fields of physics and mathematical physics. Particular emphasis is given to a general historical introduction, general continuous representations, generalized coherent states, classical and quantum correspondence, path integrals and canonical formalism. Applications are considered in quantum mechanics, optics, quantum chemistry, atomic physics, statistical physics, nuclear physics, particle physics and cosmology. A selection of original papers is reprinted.

Yang-Baxter Equation in Integrable Systems
Yang-Baxter Equation in Integrable Systems

Author: Michio Jimbo

Publisher: World Scientific

Published: 1990

Total Pages: 740

ISBN-13: 9789810201210

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This volume will be the first reference book devoted specially to the Yang-Baxter equation. The subject relates to broad areas including solvable models in statistical mechanics, factorized S matrices, quantum inverse scattering method, quantum groups, knot theory and conformal field theory. The articles assembled here cover major works from the pioneering papers to classical Yang-Baxter equation, its quantization, variety of solutions, constructions and recent generalizations to higher genus solutions.