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OverviewThis volume provides 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 includes a 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 1 is a systematic course on knots and physics starting from the ground up; and Part 2 is a set of lectures on various topics related to Part 1. Part 2 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. 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: 3rd Revised edition Volume: 1 ISBN: 9789810241117ISBN 10: 9810241119 Pages: 788 Publication Date: 26 July 2001 Audience: College/higher education , Professional and scholarly , Postgraduate, Research & Scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: Out of stock  The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available. Table of ContentsPhysical Knots; States and the Bracket Polynomial; The Jones Polynomial and Its Generalizations; Braids and the Jones Polynomial; Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quatum Group SL(2)q; Yang-Baxter Models for Specializations of the Homfly Polynomial; Knot-Crystals - Classical Knot Theory in a Modern Guise; The Kauffman Polynomial; Three Manifold Invariants from the Jones Polynomial; Integral Heuristics and Witten's Invariants; The Chromatic Polynomial; 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; and selected papers.ReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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