Knots and Physics

' 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 '