Local Operators In Integrable Models I

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Local Operators In Integrable Models I

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Author : Michio Jimbo
language : en
Publisher: American Mathematical Soc.
Release Date : 2021-07-02

Local Operators In Integrable Models I written by Michio Jimbo and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-07-02 with Education categories.

Integrable models in statistical mechanics and quantum field theory constitute a rich research field at the crossroads of modern mathematics and theoretical physics. An important issue to understand is the space of local operators in the system and, ultimately, their correlation functions and form factors. This book is the first published monograph on this subject. It treats integrable lattice models, notably the six-vertex model and the XXZ Heisenberg spin chain. A pair of fermions is introduced and used to create a basis of the space of local operators, leading to the result that all correlation functions at finite distances are expressible in terms of two transcendental functions with rational coefficients. Step-by-step explanations are given for all materials necessary for this construction, ranging from algebraic Bethe ansatz, representations of quantum groups, and the Bazhanov-Lukyanov-Zamolodchikov construction in conformal field theory to Riemann surfaces and their Jacobians. Several examples and applications are given along with numerical results. Going through the book, readers will find themselves at the forefront of this rapidly developing research field.

Local Operators In Integrable Models

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Author : MICHIO JIMBO; TETSUJI MIWA; FEDOR SMIRNOV.
language : en
Publisher:
Release Date : 1900

Local Operators In Integrable Models written by MICHIO JIMBO; TETSUJI MIWA; FEDOR SMIRNOV. and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1900 with Integral equations categories.

Local Operators In Integrable Models

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Author : Michio Jimbo
language : en
Publisher:
Release Date : 2021

Local Operators In Integrable Models written by Michio Jimbo and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021 with categories.

Form Factors In Completely Integrable Models Of Quantum Field Theory

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Author : F. A. Smirnov
language : en
Publisher: World Scientific
Release Date : 1992

Form Factors In Completely Integrable Models Of Quantum Field Theory written by F. A. Smirnov and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Science categories.

The monograph summarizes recent achievements in the calculation of matrix elements of local operators (form factors) for completely integrable models. Particularly, it deals with sine-Gordon, chiral Gross-Neven and O(3) nonlinear s models. General requirements on form factors are formulated and explicit formulas for form factors of most fundamental local operators are presented for the above mentioned models.

Integrable Systems From Classical To Quantum

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Author : John P. Harnad
language : en
Publisher: American Mathematical Soc.
Release Date : 2000

Integrable Systems From Classical To Quantum written by John P. Harnad and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.

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.

From Integrable Models To Gauge Theories

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Author : S. G. Matinyan
language : en
Publisher: World Scientific
Release Date : 2002

From Integrable Models To Gauge Theories written by S. G. Matinyan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.

"This collection of 20 articles in honour of the noted physicist and mentor Sergei Matinyan focuses on topics that are of fundamental importance to high-energy physics, field theory and cosmology. The topics range from integrable quantum field theories, three-dimensional Ising models, parton models and tests of the Standard Model, to black holes in loop quantum gravity, the cosmological constant and magnetic fields in cosmology. A pedagogical essay by Lev Okun concentrates on the problem of fundamental units. The articles have been written by experts and are addressed to graduate students and researchers."--[Source inconnue].

Characterization Of Probability Distributions On Locally Compact Abelian Groups

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Author : Gennadiy Feldman
language : en
Publisher: American Mathematical Society
Release Date : 2023-04-07

Characterization Of Probability Distributions On Locally Compact Abelian Groups written by Gennadiy Feldman and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-07 with Mathematics categories.

It is well known that if two independent identically distributed random variables are Gaussian, then their sum and difference are also independent. It turns out that only Gaussian random variables have such property. This statement, known as the famous Kac-Bernstein theorem, is a typical example of a so-called characterization theorem. Characterization theorems in mathematical statistics are statements in which the description of possible distributions of random variables follows from properties of some functions of these random variables. The first results in this area are associated with famous 20th century mathematicians such as G. Pólya, M. Kac, S. N. Bernstein, and Yu. V. Linnik. By now, the corresponding theory on the real line has basically been constructed. The problem of extending the classical characterization theorems to various algebraic structures has been actively studied in recent decades. The purpose of this book is to provide a comprehensive and self-contained overview of the current state of the theory of characterization problems on locally compact Abelian groups. The book will be useful to everyone with some familiarity of abstract harmonic analysis who is interested in probability distributions and functional equations on groups.

Algebras Lattices Varieties

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Author : Ralph S. Freese
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-03

Algebras Lattices Varieties written by Ralph S. Freese and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-03 with Mathematics categories.

This book is the third of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.

Nonlinear Evolution Equations And Dynamical Systems

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Author : Vladimir G. Makhankov
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06

Nonlinear Evolution Equations And Dynamical Systems written by Vladimir G. Makhankov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Science categories.

Proceedings of the 6th International Workshop, 16-26 July 1990, Dubna, USSR

Integrability From Statistical Systems To Gauge Theory

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Author : Patrick Dorey
language : en
Publisher:
Release Date : 2019

Integrability From Statistical Systems To Gauge Theory written by Patrick Dorey and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019 with Mathematics categories.

This volume contains lectures delivered at the Les Houches Summer School 'Integrability: from statistical systems to gauge theory' held in June 2016. The School was focussed on applications of integrability to supersymmetric gauge and string theory, a subject of high and increasing interest in the mathematical and theoretical physics communities over the past decade. Relevant background material was also covered, with lecture series introducing the main concepts and techniques relevant to modern approaches to integrability, conformal field theory, scattering amplitudes, and gauge/string duality. The book will be useful not only to those working directly on integrablility in string and guage theories, but also to researchers in related areas of condensed matter physics and statistical mechanics.