Algebraic Analysis Of Solvable Lattice Models

DOWNLOAD

Download Algebraic Analysis Of Solvable Lattice Models PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Algebraic Analysis Of Solvable Lattice Models book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page

Algebraic Analysis Of Solvable Lattice Models

DOWNLOAD
Author : Michio Jimbo
language : en
Publisher: American Mathematical Soc.
Release Date : 1994

Algebraic Analysis Of Solvable Lattice Models 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 1994 with Mathematics categories.

Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin 1/2 XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the XXX model is briefly discussed, and the book closes with a discussion of other types of models and related works.

Algebraic Analysis Of Solvable Lattice Models

DOWNLOAD
Author : Michio Jimbo
language : en
Publisher: American Mathematical Soc.
Release Date : 1995

Algebraic Analysis Of Solvable Lattice Models 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 1995 with Mathematics categories.

Based on the NSF-CBMS Regional Conference lectures presented by Miwa in June 1993, this book surveys recent developments in the interplay between solvable lattice models in statistical mechanics and representation theory of quantum affine algebras. Because results in this subject were scattered in the literature, this book fills the need for a systematic account, focusing attention on fundamentals without assuming prior knowledge about lattice models or representation theory. After a brief account of basic principles in statistical mechanics, the authors discuss the standard subjects concerning solvable lattice models in statistical mechanics, the main examples being the spin 1/2 XXZ chain and the six-vertex model. The book goes on to introduce the main objects of study, the corner transfer matrices and the vertex operators, and discusses some of their aspects from the viewpoint of physics. Once the physical motivations are in place, the authors return to the mathematics, covering the Frenkel-Jing bosonization of a certain module, formulas for the vertex operators using bosons, the role of representation theory, and correlation functions and form factors. The limit of the XXX model is briefly discussed, and the book closes with a discussion of other types of models and related works.

Rational Points On Modular Elliptic Curves

DOWNLOAD
Author : Henri Darmon
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

Rational Points On Modular Elliptic Curves written by Henri Darmon 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 2004 with Mathematics categories.

The book surveys some recent developments in the arithmetic of modular elliptic curves. It places a special emphasis on the construction of rational points on elliptic curves, the Birch and Swinnerton-Dyer conjecture, and the crucial role played by modularity in shedding light on these two closely related issues. The main theme of the book is the theory of complex multiplication, Heegner points, and some conjectural variants. The first three chapters introduce the background and prerequisites: elliptic curves, modular forms and the Shimura-Taniyama-Weil conjecture, complex multiplication and the Heegner point construction. The next three chapters introduce variants of modular parametrizations in which modular curves are replaced by Shimura curves attached to certain indefinite quaternion algebras. The main new contributions are found in Chapters 7-9, which survey the author's attempts to extend the theory of Heegner points and complex multiplication to situations where the base field is not a CM field. Chapter 10 explains the proof of Kolyvagin's theorem, which relates Heegner points to the arithmetic of elliptic curves and leads to the best evidence so far for the Birch and Swinnerton-Dyer conjecture.

Selected Topics In The Geometrical Study Of Differential Equations

DOWNLOAD
Author : Niky Kamran
language : en
Publisher: American Mathematical Soc.
Release Date : 2002-01-01

Selected Topics In The Geometrical Study Of Differential Equations written by Niky Kamran 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 2002-01-01 with Mathematics categories.

The geometrical study of differential equations has a long and distinguished history, dating back to the classical investigations of Sophus Lie, Gaston Darboux, and Elie Cartan. Currently, these ideas occupy a central position in several areas of pure and applied mathematics. In this book, the author gives an overview of a number of significant ideas and results developed over the past decade in the geometrical study of differential equations. Topics covered in the book include symmetries of differential equations and variational problems, the variational bi-complex and conservation laws, geom.

Xviith International Congress On Mathematical Physics

DOWNLOAD
Author : Arne Jensen
language : en
Publisher: World Scientific
Release Date : 2014

Xviith International Congress On Mathematical Physics written by Arne Jensen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014 with Science categories.

This is an in-depth study of not just about Tan Kah-kee, but also the making of a legend through his deeds, self-sacrifices, fortitude and foresight. This revised edition sheds new light on his political agonies in Mao's China over campaigns against capitalists and intellectuals.

Special Functions Kz Type Equations And Representation Theory

DOWNLOAD
Author : Aleksandr Nikolaevich Varchenko
language : en
Publisher: American Mathematical Soc.
Release Date :

Special Functions Kz Type Equations And Representation Theory written by Aleksandr Nikolaevich Varchenko 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 with Science categories.

Modern Trends In Algebra And Representation Theory

DOWNLOAD
Author : David Jordan
language : en
Publisher: Cambridge University Press
Release Date : 2023-08-17

Modern Trends In Algebra And Representation Theory written by David Jordan and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-08-17 with Mathematics categories.

Aimed at graduate students and non-experts, this text gives a guided tour of modern developments in algebra and representation theory.

Analysis Of Stochastic Partial Differential Equations

DOWNLOAD
Author : Davar Khoshnevisan
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-06-11

Analysis Of Stochastic Partial Differential Equations written by Davar Khoshnevisan 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 2014-06-11 with Mathematics categories.

The general area of stochastic PDEs is interesting to mathematicians because it contains an enormous number of challenging open problems. There is also a great deal of interest in this topic because it has deep applications in disciplines that range from applied mathematics, statistical mechanics, and theoretical physics, to theoretical neuroscience, theory of complex chemical reactions [including polymer science], fluid dynamics, and mathematical finance. The stochastic PDEs that are studied in this book are similar to the familiar PDE for heat in a thin rod, but with the additional restriction that the external forcing density is a two-parameter stochastic process, or what is more commonly the case, the forcing is a "random noise," also known as a "generalized random field." At several points in the lectures, there are examples that highlight the phenomenon that stochastic PDEs are not a subset of PDEs. In fact, the introduction of noise in some partial differential equations can bring about not a small perturbation, but truly fundamental changes to the system that the underlying PDE is attempting to describe. The topics covered include a brief introduction to the stochastic heat equation, structure theory for the linear stochastic heat equation, and an in-depth look at intermittency properties of the solution to semilinear stochastic heat equations. Specific topics include stochastic integrals à la Norbert Wiener, an infinite-dimensional Itô-type stochastic integral, an example of a parabolic Anderson model, and intermittency fronts. There are many possible approaches to stochastic PDEs. The selection of topics and techniques presented here are informed by the guiding example of the stochastic heat equation. A co-publication of the AMS and CBMS.

Introduction To Quantum Groups And Crystal Bases

DOWNLOAD
Author : Jin Hong
language : en
Publisher: American Mathematical Society
Release Date : 2025-02-06

Introduction To Quantum Groups And Crystal Bases written by Jin Hong 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 2025-02-06 with Mathematics categories.

The notion of a “quantum group” was introduced by V.G. Drinfel'd and M. Jimbo, independently, in their study of the quantum Yang-Baxter equation arising from 2-dimensional solvable lattice models. Quantum groups are certain families of Hopf algebras that are deformations of universal enveloping algebras of Kac-Moody algebras. And over the past 20 years, they have turned out to be the fundamental algebraic structure behind many branches of mathematics and mathematical physics, such as solvable lattice models in statistical mechanics, topological invariant theory of links and knots, representation theory of Kac-Moody algebras, representation theory of algebraic structures, topological quantum field theory, geometric representation theory, and $C^*$-algebras. In particular, the theory of “crystal bases” or “canonical bases” developed independently by M. Kashiwara and G. Lusztig provides a powerful combinatorial and geometric tool to study the representations of quantum groups. The purpose of this book is to provide an elementary introduction to the theory of quantum groups and crystal bases, focusing on the combinatorial aspects of the theory.

Braid Group Knot Theory And Statistical Mechanics Ii

DOWNLOAD
Author : Chen Ning Yang
language : en
Publisher: World Scientific
Release Date : 1994-02-24

Braid Group Knot Theory And Statistical Mechanics Ii written by Chen Ning Yang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-02-24 with Science categories.

The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on the 1989 volume but has new material included and new contributors.