Knots and Physics (eBook)
by Louis H Kauffman (Author)

 144,922 Words
 864 Pages
This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasiphysical process. The demands of knot theory, coupled with a quantumstatistical 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 new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.
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 VacuumVacuum Expectation and the Quantum Group SL(2)_{q}
 Yang–Baxter Models for Specializations of the Homfly Polynomial
 KnotCrystals — Classical Knot Theory in a 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 selected papers
Readership: Physicists and mathematicians.
 Released: November 9, 2012
 Categories: Education, Science & Nature
 Language: English
 Publisher: World Scientific Publishing Company
 ISBN10: 9814460303
 ISBN13: 9789814460309