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.
Download or read book Knots And Physics Second Edition written by Louis H Kauffman and published by World Scientific. This book was released on 1994-01-15 with total page 739 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.
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.
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.
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.
Download or read book The Interface of Knots and Physics written by Louis H. Kauffman 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.
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.
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.
Download or read book The Geometry and Physics of Knots written by Michael Francis Atiyah and published by . This book was released on 1989 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ideal Knots written by Andrzej Stasiak and published by World Scientific. This book was released on 1998 with total page 426 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter.
Download or read book New Developments in the Theory of Knots written by Toshitake Kohno and published by World Scientific. This book was released on 1990 with total page 924 pages. Available in PDF, EPUB and Kindle. Book excerpt: This reprint volume focuses on recent developments in knot theory arising from mathematical physics, especially solvable lattice models, Yang-Baxter equation, quantum group and two dimensional conformal field theory. This volume is helpful to topologists and mathematical physicists because existing articles are scattered in journals of many different domains including Mathematics and Physics. This volume will give an excellent perspective on these new developments in Topology inspired by mathematical physics.
Download or read book A Gentle Introduction To Knots Links And Braids written by Ruben Aldrovandi and published by World Scientific. This book was released on 2021-10-14 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Interface of Knots and Physics written by University of Illinois Staff and published by . This book was released on 2000-08 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Knot Theory written by Vassily Olegovich Manturov and published by CRC Press. This book was released on 2018-04-17 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory’s state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.
Download or read book Adex Theory How The Ade Coxeter Graphs Unify Mathematics And Physics written by Saul-paul Sirag and published by World Scientific. This book was released on 2016-01-25 with total page 277 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how the ADE Coxeter graphs unify at least 20 different types of mathematical structures. These mathematical structures are of great utility in unified field theory, string theory, and other areas of physics.
Download or read book Linknot Knot Theory By Computer written by Slavik Vlado Jablan and published by World Scientific. This book was released on 2007-11-16 with total page 497 pages. Available in PDF, EPUB and Kindle. Book excerpt: LinKnot — Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics.The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves.Hands-on computations using Mathematica or the webMathematica package LinKnot and beautiful illustrations facilitate better learning and understanding. LinKnot is also a powerful research tool for experimental mathematics implementation of Caudron's ideas. The use of Conway notation enables experimenting with large families of knots and links.Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata.
Download or read book Energy Of Knots And Conformal Geometry written by Jun O'hara and published by World Scientific. This book was released on 2003-03-25 with total page 306 pages. Available in PDF, EPUB and Kindle. Book excerpt: Energy of knots is a theory that was introduced to create a “canonical configuration” of a knot — a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a “canonical configuration” of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments.
