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Quantum Inverse Scattering Method And Correlation Functions
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Book Synopsis Quantum Inverse Scattering Method and Correlation Functions by : V. E. Korepin
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.
Book Synopsis L. D. Faddeev's Seminar on Mathematical Physics by : Michael Semenov-Tian-Shansky
Download or read book L. D. Faddeev's Seminar on Mathematical Physics written by Michael Semenov-Tian-Shansky and published by American Mathematical Soc.. This book was released on 2000 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Professor L. D. Faddeev's seminar at Steklov Mathematical Institute (St. Petersburg, Russia) has a long history of over 30 years of intensive work which shaped modern mathematical physics. This collection, honoring Professor Faddeev's 65th anniversary, has been prepared by his students and colleagues. Topics covered in the volume include classical and quantum integrable systems (both analytic and algebraic aspects), quantum groups and generalizations, quantum field theory, and deformation quantization. Included is a history of the seminar highlighting important developments, such as the invention of the quantum inverse scattering method and of quantum groups. The book will serve nicely as a comprehensive, up-to-date resource on the topic.
Book Synopsis Spinning Strings and Correlation Functions in the AdS/CFT Correspondence by : Juan Miguel Nieto
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 187 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.
Book Synopsis Inverse Scattering and Applications by : David H. Sattinger
Download or read book Inverse Scattering and Applications written by David H. Sattinger and published by American Mathematical Soc.. This book was released on 1991 with total page 133 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of an AMS-IMS-SIAM Summer Institute on Inverse Scattering and Applications, held in Amherst, Massachusetts, in June 1990. The papers cover the current state of the art in inverse conductivity problems, applications of inverse scattering theory to integrable systems, three-dimensional inverse scattering, inverse monodromy problems, and nonlinear waves, among other topics. Intended for researchers working in inverse scattering theory, inverse conductance problems, and completely integrable systems, this book presents results by some of the major experts in the field.
Book Synopsis Lie Theory and Its Applications in Physics by : Vladimir Dobrev
Download or read book Lie Theory and Its Applications in Physics written by Vladimir Dobrev and published by Springer. This book was released on 2015-01-26 with total page 571 pages. Available in PDF, EPUB and Kindle. Book excerpt: Traditionally, Lie theory is a tool to build mathematical models for physical systems. Recently, the trend is towards geometrization of the mathematical description of physical systems and objects. A geometric approach to a system yields in general some notion of symmetry which is very helpful in understanding its structure. Geometrization and symmetries are meant in their widest sense, i.e., representation theory, algebraic geometry, infinite-dimensional Lie algebras and groups, superalgebras and supergroups, groups and quantum groups, noncommutative geometry, symmetries of linear and nonlinear PDE, special functions, and others. Furthermore, the necessary tools from functional analysis and number theory are included. This is a big interdisciplinary and interrelated field. Samples of these fresh trends are presented in this volume, based on contributions from the Workshop "Lie Theory and Its Applications in Physics" held near Varna (Bulgaria) in June 2013. This book is suitable for a broad audience of mathematicians, mathematical physicists, and theoretical physicists and researchers in the field of Lie Theory.
Book Synopsis Correlations in Low-Dimensional Quantum Gases by : Guillaume Lang
Download or read book Correlations in Low-Dimensional Quantum Gases written by Guillaume Lang and published by Springer. This book was released on 2018-12-29 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book addresses several aspects of thermodynamics and correlations in the strongly-interacting regime of one-dimensional bosons, a topic at the forefront of current theoretical and experimental studies. Strongly correlated systems of one-dimensional bosons have a long history of theoretical study. Their experimental realisation in ultracold atom experiments is the subject of current research, which took off in the early 2000s. Yet these experiments raise new theoretical questions, just begging to be answered. Correlation functions are readily available for experimental measurements. In this book, they are tackled by means of sophisticated theoretical methods developed in condensed matter physics and mathematical physics, such as bosonization, the Bethe Ansatz and conformal field theory. Readers are introduced to these techniques, which are subsequently used to investigate many-body static and dynamical correlation functions.
Book Synopsis Statistical Mechanics And Field Theory - Proceedings Of The Seventh Physics Summer School by : Bazhanov Vladimir V
Download or read book Statistical Mechanics And Field Theory - Proceedings Of The Seventh Physics Summer School written by Bazhanov Vladimir V and published by World Scientific. This book was released on 1995-12-21 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This proceedings volume aims to expose graduate students to the basic ideas of field theory and statistical mechanics and to give them an understanding and appreciation of current topical research.
Book Synopsis Yang-baxter Equations, Conformal Invariance And Integrability In Statistical Mechanics And Field Theory - Proceedings Of A Conference by : Barber Michael N
Download or read book Yang-baxter Equations, Conformal Invariance And Integrability In Statistical Mechanics And Field Theory - Proceedings Of A Conference written by Barber Michael N and published by #N/A. This book was released on 1990-05-01 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Factorization and Integrable Systems by : Israel Gohberg
Download or read book Factorization and Integrable Systems written by Israel Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 227 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume comprises the specially prepared lecture notes of a a Summer School on "Factorization and Integrable Systems" held in September 2000 at the University of Algarve in Portugal. The main aim of the school was to review the modern factorization theory and its application to classical and quantum integrable systems. The program consisted of a number of short courses given by leading experts in the field.
Book Synopsis Quantum Field Theory And Condensed Matter Physics: Proceedings Of The 4th Trieste Conference by : Seifallah Randjbar-daemi
Download or read book Quantum Field Theory And Condensed Matter Physics: Proceedings Of The 4th Trieste Conference written by Seifallah Randjbar-daemi and published by World Scientific. This book was released on 1994-03-29 with total page 150 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this interdisciplinary conference was to bring together experts in quantum field theory and condensed matter physics to survey the latest exciting developments in this border-line field, such as the Chern-Simons field theory and quantum hall effect, anyon superconductivity, Yang-Baxter equations and quantum groups, conformal field theory and multi-channel kondo effect, matrix models and quantum gravity, etc.This set of proceedings contains brief reviews contributed by leading experts in the field.
Book Synopsis MathPhys Odyssey 2001 by : Masaki Kashiwara
Download or read book MathPhys Odyssey 2001 written by Masaki Kashiwara and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'MathPhys Odyssey 2001' will serve as an excellent reference text for mathematical physicists and graduate students in a number of areas.; Kashiwara/Miwa have a good track record with both SV and Birkhauser.
Book Synopsis Mapping of Parent Hamiltonians by : Martin Greiter
Download or read book Mapping of Parent Hamiltonians written by Martin Greiter and published by Springer. This book was released on 2011-12-04 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph introduces an exact model for a critical spin chain with arbitrary spin S, which includes the Haldane--Shastry model as the special case S=1/2. While spinons in the Haldane-Shastry model obey abelian half-fermi statistics, the spinons in the general model introduced here obey non-abelian statistics. This manifests itself through topological choices for the fractional momentum spacings. The general model is derived by mapping exact models of quantized Hall states onto spin chains. The book begins with pedagogical review of all the relevant models including the non-abelian statistics in the Pfaffian Hall state, and is understandable to every student with a graduate course in quantum mechanics.
Book Synopsis Encyclopedia of Nonlinear Science by : Alwyn Scott
Download or read book Encyclopedia of Nonlinear Science written by Alwyn Scott and published by Routledge. This book was released on 2006-05-17 with total page 1107 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 438 alphabetically-arranged essays, this work provides a useful overview of the core mathematical background for nonlinear science, as well as its applications to key problems in ecology and biological systems, chemical reaction-diffusion problems, geophysics, economics, electrical and mechanical oscillations in engineering systems, lasers and nonlinear optics, fluid mechanics and turbulence, and condensed matter physics, among others.
Book Synopsis Statistical Models, Yang–Baxter Equation and Related Topics; Symmetry, Statistical Mechanical Models and Applications by : M L Ge
Download or read book Statistical Models, Yang–Baxter Equation and Related Topics; Symmetry, Statistical Mechanical Models and Applications written by M L Ge and published by World Scientific. This book was released on 1996-09-20 with total page 460 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the proceedings of two international conferences: a satellite meeting of the IUPAP Statphys-19 Conference and the Seventh Nankai Workshop, held in Tianjin, China in August 1995. The central theme of the two conferences, which drew participants from 18 countries, was the Yang–Baxter equation and its development and applications. With topics ranging from quantum groups, vertex and spin models, to applications in condensed matter physics, this book reflects the current research interest of integrable systems in statistical mechanics. Contents:Satellite Meeting of Statphys-19:Boundary Yang–Baxter in the RSOS/SOS Representation (C Ahn & W M Koo)Quantum Domains in Ferromagnetic Anisotropic Heisenberg Chains (F C Alcaraz et al.)The Generalized Chiral Clock Model and Its Phase Diagram (H Au-Yang & J H H Perk)Algebraic Solution of the Coincidence Problem for Crystals and Quasicrystals (M Baake)Reflection Equations and Surface Critical Phenomena (M T Batchelor)Quantum Field Theories in Terms of Group-Valued Local Fields: An Overview (L-L Chau)U(1)-Invariant Local and Integrable Lattice Formulation of the Massive Thirring Model (C Destri)Dilute Algebras and Solvable Lattice Models (U Grimm)Mutual Exclusion Statistics in the Exactly Solvable Model of the Mott Metal-Insulator Transition (Y Hatsugai et al.) Quantum Group and the Hofstadter Problem (Y Hatsugai et al.)Domain Walls in the Spin-S Quantum Ising Chain (M Henkel)Probability of Phase Separation and Two Point Temperature Correlation Functions for the Bose Gas with Delta Interaction (A R Its & V E Korepin)Stochastic Reaction-Diffusion Processes, Operator Algebras and Integrable Quantum Spin Chains (G M Schütz)Vertex-Face Correspondence in Elliptic Solutions of the Yang–Baxter Equation (Y Shibukawa)Logarithmic Anomalies of Susceptibility for Solvable Models (M Takahashi)On Chiral Hubbard Model at Strong Interaction (D F Wang)Soluble Free-Fermion Models in d Dimensions (F Y Wu)Bosonization Based on Bethe Ansatz Equations and Proof of the Conformal Conjecture (Y-S Wu & Y Yu)and other papersThe Seventh Nankai Workshop:Corner Transfer Matrix of Asymmetric Vertex Models (H-P Eckle)Scaling Properties of the Ising Model in a Field (U Grimm & B Nienhuis)One Dimensional Lattice Models of Electrons with r–2 Hopping and Exchange (Ch Gruber & D F Wang)Symmetry Group Invariants for Spontaneous Magnetization (J-M Maillard)Experimental Realizations of Integrable Reaction-Diffusion Processes in Biological and Chemical Systems (G M Schütz)Zamolodchikov–Faddeev Algebra in 2-Component Anyons (Y-L Shen & M-L Ge)and other papers Readership: Theoretical physicists and mathematicians. keywords:
Book Synopsis Integrable Systems by : John P. Harnad
Download or read book Integrable Systems written by John P. Harnad and published by American Mathematical Soc.. This book was released on with total page 284 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 Important Developments in Soliton Theory by : A.S. Fokas
Download or read book Important Developments in Soliton Theory written by A.S. Fokas and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 563 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the last ten to fifteen years there have been many important developments in the theory of integrable equations. This period is marked in particular by the strong impact of soliton theory in many diverse areas of mathematics and physics; for example, algebraic geometry (the solution of the Schottky problem), group theory (the discovery of quantum groups), topology (the connection of Jones polynomials with integrable models), and quantum gravity (the connection of the KdV with matrix models). This is the first book to present a comprehensive overview of these developments. Numbered among the authors are many of the most prominent researchers in the field.
Book Synopsis Planar Ising Correlations by : John Palmer
Download or read book Planar Ising Correlations written by John Palmer and published by Springer Science & Business Media. This book was released on 2007-07-27 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steady progress in recent years has been made in understanding the special mathematical features of certain exactly solvable models in statistical mechanics and quantum field theory, including the scaling limits of the 2-D Ising (lattice) model, and more generally, a class of 2-D quantum fields known as holonomic fields. New results have made it possible to obtain a detailed nonperturbative analysis of the multi-spin correlations. In particular, the book focuses on deformation analysis of the scaling functions of the Ising model, and will appeal to graduate students, mathematicians, and physicists interested in the mathematics of statistical mechanics and quantum field theory.
