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OverviewThis book is an introduction to 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 framework, create a context that naturally includes a wide range of interrelated 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 two parts: Part one is a systematic course in knots and physics starting from the ground up. Part two is a set of lectures on various topics related with and sometimes based on part one. It also explores some side-topies such as frictional properties of knots, relations with combinatorics, knots and dynamical systems. In this second edition, an appendix has been added with a discussion of invariants of embedded graphs and Vassiliev invariants. Included is a reprinting of three recent papers by the author on quantum groups and invariants of 3-manifolds, spin networks and graph invariants. Full Product DetailsAuthor: Louis H Kauffman (Univ Of Illinois At Chicago, Usa)Publisher: World Scientific Publishing Co Pte Ltd Imprint: World Scientific Publishing Co Pte Ltd Edition: Second Edition Volume: 1 Dimensions: Width: 16.00cm , Height: 4.30cm , Length: 22.00cm Weight: 1.111kg ISBN: 9789810216566ISBN 10: 9810216564 Pages: 740 Publication Date: 01 January 1994 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: In Print  This item will be ordered in for you from one of our suppliers. Upon receipt, we will promptly dispatch it out to you. For in store availability, please contact us. Table of ContentsPhysical Knots; States and the Bracket Polynomial; The Jones Polynominal and Its Generalizations; Braids and Polynomials: Formal Feynman Diagrams, Bracket as Vacuum-Vacmum expectation and the Quantum Group SL(2)q; Yang-Baxter Models for Specialization's of the Homfly Polynomial; The Alexander Polynomial; Knot Crystals - Classical Knot Theory in Modem Guise; The Kauffman Polynomial; Three-Manifold Invariants from the Jones Polynomials; integral Heuristics and Witten's lnvariants; Chromatic Polynomials; The Potts Model and the Dichromatic Polynomial; The Penrose Theory of Spin Networks; Knots and Strings - Knotted Strings; DNA and Quantum Field Theory; Knots in Dynamical Systems - The Lorenz Attractor.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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