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Knots And Physics
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Book Synopsis Knots and Physics by : Louis H Kauffman
Download or read book Knots and Physics written by Louis H Kauffman and published by World Scientific. This book was released on 1994-01-15 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included. This book is an introduction to knot and link invariants as generalized amplitudes (vacuum–vacuum 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 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 to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems. 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 PolynomialThe Alexander PolynomialKnot-Crystals — Classical Knot Theory in 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 other papers Readership: Physicists, mathematical physicists and mathematicians. keywords: Reviews of the First 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 “… 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
Book Synopsis The Geometry and Physics of Knots by : Michael Francis Atiyah
Download or read book The Geometry and Physics of Knots written by Michael Francis Atiyah and published by Cambridge University Press. This book was released on 1990-08-23 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.
Book Synopsis History and Science of Knots by : J C Turner
Download or read book History and Science of Knots written by J C Turner and published by World Scientific. This book was released on 1996-05-30 with total page 464 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book brings together twenty essays on diverse topics in the history and science of knots. It is divided into five parts, which deal respectively with knots in prehistory and antiquity, non-European traditions, working knots, the developing science of knots, and decorative and other aspects of knots. Its authors include archaeologists who write on knots found in digs of ancient sites (one describes the knots used by the recently discovered Ice Man); practical knotters who have studied the history and uses of knots at sea, for fishing and for various life support activities; a historian of lace; a computer scientist writing on computer classification of doilies; and mathematicians who describe the history of knot theories from the eighteenth century to the present day. In view of the explosion of mathematical theories of knots in the past decade, with consequential new and important scientific applications, this book is timely in setting down a brief, fragmentary history of mankind's oldest and most useful technical and decorative device — the knot. Contents:Prehistory and Antiquity:Pleistocene KnottingWhy Knot? — Some Speculations on the First KnotsOn Knots and Swamps — Knots in European PrehistoryAncient Egyptian Rope and KnotsNon-European Traditions:The Peruvian QuipuThe Art of Chinese Knots Works: A Short HistoryInuit KnotsWorking Knots:Knots at SeaA History of Life Support KnotsTowards a Science of Knots?:Studies on the Behaviour of KnotsA History of Topological Knot Theory of KnotsTramblesCrochet Work — History and Computer ApplicationsDecorative Knots and Other Aspects:The History of MacraméA History of LaceHeraldic KnotsOn the True Love Knotand other papers Readership: Mathematicians, archeologists, social historians and general readers. keywords:Antiquit;Braiding;Climbing;Heraldry;History;Knots;Lace;Mariners;Prehistory;Quipus;Science;Theory;Topology;Knotting, Pleistocene;Egyptian;Inuit;Chinese;Mountaineering, Topological Knot Theory;Knot Theories;Quipo Knot Mathematics;Knot Strength Efficiency;Heraldic;True Love;Crochet;Computer Aided Design;Trambles “… it is a veritable compendium of information about every aspects of knots, from their links with quantum theory to attempts to measure their strength when tying climbing ropes together … the huge scope of this book makes it one I have turned to many times, for many different purposes.” New Scientists “I enjoyed browsing through all the chapters. They contain material that a mathematician would not normally come across in his work.” The Mathematical Intelligencer
Book Synopsis The Knot Book by : Colin Conrad Adams
Download or read book The Knot Book written by Colin Conrad Adams and published by American Mathematical Soc.. This book was released on 2004 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt: Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.
Book Synopsis Knots and Physics by : Louis H. Kauffman
Download or read book Knots and Physics written by Louis H. Kauffman and published by World Scientific. This book was released on 2013 with total page 865 pages. Available in PDF, EPUB and Kindle. Book excerpt: An introduction to knot and link invariants as generalised 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.
Book Synopsis Knots and Feynman Diagrams by : Dirk Kreimer
Download or read book Knots and Feynman Diagrams written by Dirk Kreimer and published by Cambridge University Press. This book was released on 2000-07-20 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explains how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. The author emphasizes how new discoveries in mathematics have inspired conventional calculational methods for perturbative quantum field theory to become more elegant and potentially more powerful methods. The material illustrates what may possibly be the most productive interface between mathematics and physics. As a result, it will be of interest to graduate students and researchers in theoretical and particle physics as well as mathematics.
Download or read book On Knots written by Louis H. Kauffman and published by Princeton University Press. This book was released on 1987 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: On Knots is a journey through the theory of knots, starting from the simplest combinatorial ideas--ideas arising from the representation of weaving patterns. From this beginning, topological invariants are constructed directly: first linking numbers, then the Conway polynomial and skein theory. This paves the way for later discussion of the recently discovered Jones and generalized polynomials. The central chapter, Chapter Six, is a miscellany of topics and recreations. Here the reader will find the quaternions and the belt trick, a devilish rope trick, Alhambra mosaics, Fibonacci trees, the topology of DNA, and the author's geometric interpretation of the generalized Jones Polynomial. Then come branched covering spaces, the Alexander polynomial, signature theorems, the work of Casson and Gordon on slice knots, and a chapter on knots and algebraic singularities.The book concludes with an appendix about generalized polynomials.
Book Synopsis Knots and Applications by : Louis H. Kauffman
Download or read book Knots and Applications written by Louis H. Kauffman and published by World Scientific. This book was released on 1995 with total page 502 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory.
Book Synopsis Introductory Lectures on Knot Theory by : Louis H. Kauffman
Download or read book Introductory Lectures on Knot Theory written by Louis H. Kauffman and published by World Scientific. This book was released on 2012 with total page 577 pages. Available in PDF, EPUB and Kindle. Book excerpt: More recently, Khovanov introduced link homology as a generalization of the Jones polynomial to homology of chain complexes and Ozsvath and Szabo developed Heegaard-Floer homology, that lifts the Alexander polynomial. These two significantly different theories are closely related and the dependencies are the object of intensive study. These ideas mark the beginning of a new era in knot theory that includes relationships with four-dimensional problems and the creation of new forms of algebraic topology relevant to knot theory. The theory of skein modules is an older development also having its roots in Jones discovery. Another significant and related development is the theory of virtual knots originated independently by Kauffman and by Goussarov Polyak and Viro in the '90s. All these topics and their relationships are the subject of the survey papers in this book.
Book Synopsis Knots And Physics (Third Edition) by : Louis H Kauffman
Download or read book Knots And Physics (Third Edition) written by Louis H Kauffman and published by World Scientific. This book was released on 2001-07-26 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book is an introduction to knot and link invariants as generalised 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 third edition, a paper by the author entitled “Knot Theory and Functional Integration” has been added. This paper shows how the Kontsevich integral approach to the Vassiliev invariants is directly related to the perturbative expansion of Witten's functional integral. While the book supplies the background, this paper can be read independently as an introduction to quantum field theory and knot invariants and their relation to quantum gravity. As in the second edition, there is a selection of papers by the author at the end of the book. Numerous clarifying remarks have been added to the text.
Author :W.B.Raymond Lickorish Publisher :Springer Science & Business Media ISBN 13 :146120691X Total Pages :213 pages Book Rating :4.4/5 (612 download)
Book Synopsis An Introduction to Knot Theory by : W.B.Raymond Lickorish
Download or read book An Introduction to Knot Theory written by W.B.Raymond Lickorish and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 213 pages. Available in PDF, EPUB and Kindle. Book excerpt: A selection of topics which graduate students have found to be a successful introduction to the field, employing three distinct techniques: geometric topology manoeuvres, combinatorics, and algebraic topology. Each topic is developed until significant results are achieved and each chapter ends with exercises and brief accounts of the latest research. What may reasonably be referred to as knot theory has expanded enormously over the last decade and, while the author describes important discoveries throughout the twentieth century, the latest discoveries such as quantum invariants of 3-manifolds as well as generalisations and applications of the Jones polynomial are also included, presented in an easily intelligible style. Readers are assumed to have knowledge of the basic ideas of the fundamental group and simple homology theory, although explanations throughout the text are numerous and well-done. Written by an internationally known expert in the field, this will appeal to graduate students, mathematicians and physicists with a mathematical background wishing to gain new insights in this area.
Author :American Mathematical Society Publisher :American Mathematical Soc. ISBN 13 :0821803808 Total Pages :221 pages Book Rating :4.8/5 (218 download)
Book Synopsis The Interface of Knots and Physics by : American Mathematical Society
Download or read book The Interface of Knots and Physics written by American Mathematical Society and published by American Mathematical Soc.. This book was released on 1996 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text is the result of an AMS Short Course on Knots and Physics that was held in San Francisco in January 1994. The authors use ideas and methods of mathematical physics to extract topological information about knots and manifolds. The book features a basic introduction to knot polynomials in relation to statistical link invariants as well as concise introductions to topological quantum field theories and to the role of knot theory in quantum gravity.
Book Synopsis Knot Theory and Its Applications by : Kunio Murasugi
Download or read book Knot Theory and Its Applications written by Kunio Murasugi and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.
Book Synopsis The Mathematics of Knots by : Markus Banagl
Download or read book The Mathematics of Knots written by Markus Banagl and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.
Author :Alekseĭ Bronislavovich Sosinskiĭ Publisher :Harvard University Press ISBN 13 :9780674009448 Total Pages :158 pages Book Rating :4.0/5 (94 download)
Book Synopsis Knots by : Alekseĭ Bronislavovich Sosinskiĭ
Download or read book Knots written by Alekseĭ Bronislavovich Sosinskiĭ and published by Harvard University Press. This book was released on 2002 with total page 158 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, written by a mathematician known for his own work on knot theory, is a clear, concise, and engaging introduction to this complicated subject, and a guide to the basic ideas and applications of knot theory. 63 illustrations.
Book Synopsis Chemistry Made Easy - Vol 1 by : Math-Knots LLC
Download or read book Chemistry Made Easy - Vol 1 written by Math-Knots LLC and published by . This book was released on 2019-04-22 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Tying Light in Knots by : David S Simon
Download or read book Tying Light in Knots written by David S Simon and published by Morgan & Claypool Publishers. This book was released on 2018-11-06 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: Topology is the study of properties of geometrical objects that remain invariant as the object is bent, twisted, or otherwise continuously deformed. It has been an indispensable tool in particle physics and solid state physics for decades, but in recent years it has become increasingly relevant in classical and quantum optics as well. It makes appearances through such diverse phenomena as Pancharatnam-Berry phases, optical vortices and solitons, and optical simulations of solid-state topological phenomena. This book concisely provides the necessary mathematical background needed to understand these developments and to give a rapid survey of some of the optical applications where topological issues arise.
