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.

Contents:

• Physical 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 Quantum Group SL(2)q
• Yang-Baxter Models for Specializations of the Homfly Polynomial
• The Alexander Polynomial
• Knot-Crystals — Classical Knot Theory in 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 other papers

Reviews of the First Edition

"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."

"... 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."