Knots And Physics (Third Edition)
World Scientific, 26.07.2001 - 788 Seiten
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.
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3-manifolds 4-valent abstract tensor Alexander polynomial ambient isotopy bracket polynomial braid group calculation colors combinatorial completes the proof components compute construction corresponding crossing defined diagrammatic dimensional edge element embedding equivalent evaluation example field theory Figure formalism formula functional integral gauge given graph G Hence Homfly polynomial Hopf algebra identity index set indices isotopy invariant Jones polynomial knot or link knot theory knots and links L. H. Kauffman labelled Lie algebra link diagram link invariants Math matrix multiplication nodes Note obtained Phys planar graph plane Preprint Proposition quantum groups quaternions R-matrix recoupling theory regular isotopy regular isotopy invariant Reidemeister moves relation representation rotation shown space spin network strands string structure summation tangle Temperley-Lieb algebra Theorem trefoil tunnel link Turaev twist unknot unoriented Vassiliev invariants vector vertex weights vertices Wilson loop Witten Yang-Baxter Equation zero