Braid Group Knot Theory And Statistical Mechanics Ii
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Braid Group Knot Theory And Statistical Mechanics Ii
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Author : Chen Ning Yang
language : en
Publisher: World Scientific
Release Date : 1994
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 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.
Braid Group Knot Theory And Statistical Mechanics
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Author : Chen Ning Yang
language : en
Publisher: World Scientific
Release Date : 1989
Braid Group Knot Theory And Statistical Mechanics 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 1989 with Braid theory categories.
This volume covers the cross fertilization of ideas in physics and in mathematics. It contains single volume articles by workers in the field of statistical mechanics who have very different approaches.
Braid Group Knot Theory And Statistical Mechanics
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Author : C. N. Yang
language : en
Publisher:
Release Date : 1989
Braid Group Knot Theory And Statistical Mechanics written by C. N. Yang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1989 with categories.
New Developments In The Theory Of Knots
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Author :
language : en
Publisher:
Release Date :
New Developments In The Theory Of Knots written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
Subfactors And Knots
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Author : Vaughan F. R. Jones
language : en
Publisher: American Mathematical Soc.
Release Date : 1991
Subfactors And Knots written by Vaughan F. R. Jones 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 1991 with Mathematics categories.
This book is based on a set of lectures presented by the author at the NSF-CBMS Regional Conference, Applications of Operator Algebras to Knot Theory and Mathematical Physics, held at the U.S. Naval Academy in Annapolis in June 1988. The audience consisted of low-dimensional topologists and operator algebraists, so the speaker attempted to make the material comprehensible to both groups. He provides an extensive introduction to the theory of von Neumann algebras and to knot theory and braid groups. The presentation follows the historical development of the theory of subfactors and the ensuing applications to knot theory, including full proofs of some of the major results. The author treats in detail the Homfly and Kauffman polynomials, introduces statistical mechanical methods on knot diagrams, and attempts an analogy with conformal field theory. Written by one of the foremost mathematicians of the day, this book will give readers an appreciation of the unexpected interconnections between different parts of mathematics and physics.
A Gentle Introduction To Knots Links And Braids
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Author : Ruben Aldrovandi
language : en
Publisher: World Scientific
Release Date : 2021-10-14
A Gentle Introduction To Knots Links And Braids written by Ruben Aldrovandi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-14 with Science categories.
The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
Braid Group Knot Theory And Statistical Mechanics
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Author : C N Yang
language : en
Publisher: World Scientific
Release Date : 1991-06-05
Braid Group Knot Theory And Statistical Mechanics written by C N 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 1991-06-05 with categories.
Contents:Notes on Subfactors and Statistical Mechanics (V F R Jones)Polynomial Invariants in Knot Theory (L H Kauffman)Algebras of Loops on Surfaces, Algebras of Knots, and Quantization (V G Turaev)Quantum Groups (L Faddeev et al.)Introduction to the Yang-Baxter Equation (M Jimbo)Integrable Systems Related to Braid Groups and Yang-Baxter Equation (T Kohno)The Yang-Baxter Relation: A New Tool for Knot Theory (Y Akutsu et al.)Akutsu-Wadati Link Polynomials from Feynman-Kauffman Diagrams (M-L Ge et al.)Quantum Field Theory and the Jones Polynomial (E Witten) Readership: Mathematical physicists.
Knots And Physics
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Author : Louis H Kauffman
language : en
Publisher: World Scientific
Release Date : 2012-11-09
Knots And Physics written by Louis H Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-11-09 with Science categories.
This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasi-physical process. The demands of knot theory, coupled with a quantum-statistical framework, create a context that naturally and powerfully includes an extraordinary range of interrelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward knot theory and its relations with these subjects. This stance has the advantage of providing direct access to the algebra and to the combinatorial topology, as well as physical ideas. The book is divided into two parts: Part I is a systematic course on knots and physics starting from the ground up, and Part II is a set of lectures on various topics related to Part I. Part II includes topics such as frictional properties of knots, relations with combinatorics, and knots in dynamical systems. In this new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added. Contents:Physical KnotsStates and the Bracket PolynomialThe Jones Polynomial and Its GeneralizationsBraids and the Jones PolynomialFormal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)qYang–Baxter Models for Specializations of the Homfly PolynomialKnot-Crystals — Classical Knot Theory in a Modern GuiseThe Kauffman PolynomialThree Manifold Invariants from the Jones PolynomialIntegral Heuristics and Witten's InvariantsThe Chromatic PolynomialThe Potts Model and the Dichromatic PolynomialThe Penrose Theory of Spin NetworksKnots and Strings — Knotted StringsDNA and Quantum Field TheoryKnots in Dynamical Systems — The Lorenz Attractorand selected papers Readership: Physicists and mathematicians. Keywords:Knots;Kauffman;Jones PolynomialReviews: "This book is an essential volume for the student of low-dimensional topology from which a serious student can learn most aspects of modern knot theory. Its informal tone encourages investigation on the part of the reader. The author leaves the reader items to puzzle out." Mathematical Reviews Reviews of the Third Edition: “It is an attractive book for physicists with profuse and often entertaining illustrations … proofs … seldom heavy and nearly always well explained with pictures … succeeds in infusing his own excitement and enthusiasm for these discoveries and their potential implications.” Physics Today “The exposition is clear and well illustrated with many examples. The book can be recommended to everyone interested in the connections between physics and topology of knots.” Mathematics Abstracts “… here is a gold mine where, with care and patience, one should get acquainted with a beautiful subject under the guidance of a most original and imaginative mind.” Mathematical Reviews
Knots And Physics
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Author : Louis H Kauffman
language : en
Publisher: World Scientific
Release Date : 1991-06-25
Knots And Physics written by Louis H Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991-06-25 with categories.
' This book is an introductory explication on the theme of knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical frame work create a context that naturally and powerfully includes an extraordinary range of interelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward the knot theory and its relations with these subjects. This has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related with and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics, knots in dynamical systems. Contents:Physical KnotsStates and the Bracket PolynomialThe Jones Polynomial and Its GeneralizationsBraids and the Jones PolynomialFormal Feynman Diagrams, Bracket as Vacuum-Vacuum Expectation and the Quantum Group SL(2)qYang-Baxter Models for Specializations of the Homfly PolynomialsThe Alexander PolynomialKnot-Crystals — Classical Knot Theory in Modern GuiseIntegral Heuristics and Witten's InvariantsThe Chromatic PolynomialThe Potts Model and the Dichromatic PolynomialThe Penrose Theory of Spin NetworksConformal Field Theory and Topology, and others Readership: Mathematical physicists and topologists. Keywords:QFT;Dynamical Systems;Knots;Jones Polynomial;Yang-Baxter Models;Alexander Polynomial;Potts Model;Knotted Strings;DNA “… a very readable introduction to recent research on the interaction between mathematics and mathematical physics… it succeeds in telling the story, in a way that maximizes its accessibility, of how knots and physics have recently come together. ” Science “It is an attractive book for physicists with profuse and often entertaining illustrations … proofs … seldom heavy and nearly always well explained with pictures… succeeds in infusing his own excitement and enthusiasm for these discoveries and their potential implications.” Physics Today “I find the book to be excellent value for its price. Kauffman manages to take the reader from the most elementary (and physically useful) knots to the most recent developments at the very forefront of a rapidly expanding field … It deserves to be a classic.” Australian & New Zealand Physicist “The exposition is clear and well illustrated with many examples. The book can be recommended to everyone interested in the connections between physics and topology of knots.” Mathematics Abstracts “His writing is as relaxed and good-humoured as mathematical prose can be, and the reader is encouraged, by the general style of presentation and by exercises embedded in the text, to develop both intuition and facility at manipulating the formalism.” Contemporary Physics “… here is a gold mine where, with care and patience, one should get acquainted with a beautiful subject under the guidance of a most original and imaginative mind.” Mathematical Reviews '
An Introduction To Knot Theory
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Author : W.B.Raymond Lickorish
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-10-03
An Introduction To Knot Theory written by W.B.Raymond Lickorish 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 1997-10-03 with Mathematics categories.
Exercises in each chapter