Knots And Physics (Second Edition)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. |
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3-manifolds 4-valent Alexander polynomial ambient isotopy bracket polynomial braid group calculation colors completes the proof components compute construction corresponding crossing defined diagrammatic dimensional edge element embedding equivalent evaluation example field theory Figure follows formalism formula function gauge given Hence Homfly polynomial Hopf algebra identity index set indices integral isotopy invariant Jones polynomial Jordan curve knot or link knot theory knots and links L. H. Kauffman labelled Lie algebra link diagram link invariants loop Math matrix mirror image multiplication nodes Note obtained oriented link Phys planar graph plane Preprint Proposition quantum groups quaternions R-matrix recoupling theory regular isotopy regular isotopy invariant Reidemeister moves relation representation rotation shown solution space spin network strands string structure summation tangle Temperley Temperley-Lieb algebra Theorem topological tree trefoil tunnel link Turaev twist unknot unoriented vector vertex weights vertices Yang-Baxter Equation