Knots and Physics

New Edition: Knots and Physics (4th Edition)

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.

• Physical Knots
• States and the Bracket Polynomial
• The Jones Polynomial and Its Generalizations
• Braids and the Jones Polynomial
• Formal Feynman Diagrams, Bracket as Vacuum-Vacuum Expectation and the Quantum Group SL(2)q
• Yang-Baxter Models for Specializations of the Homfly Polynomials
• The Alexander Polynomial
• Knot-Crystals — Classical Knot Theory in Modern Guise
• Integral Heuristics and Witten's Invariants
• The Chromatic Polynomial
• The Potts Model and the Dichromatic Polynomial
• The Penrose Theory of Spin Networks
• Conformal Field Theory and Topology, and others