Knots And Physics (Fourth Edition)

By: Louis H Kauffman

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Paperback | 14 November 2012 | Edition Number 4

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866 Pages

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Revised

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22.7 x 15.2 x 5.5

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This invaluable book is an introduction to knot and link invariants as generalized 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 new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.

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Non-Fiction Mathematics Topology Algebraic Topology Science Physics Geometry Algebraic Geometry Booktopia Publisher Services World Scientific Publishing

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Published: 24th November 2012

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Preface to the First Edition	p. vii
Preface to the Second Edition	p. xi
Preface to the Third Edition	p. xiii
Preface to the Fourth Edition	p. xv
A Short Course of Knots and Physics
Physical Knots	p. 4
Diagrams and Moves	p. 8
States and the Bracket Polynomial	p. 25
Alternating Links and Checkerboard Surfaces	p. 39
The Jones Polynomial and its Generalizations	p. 49
An Oriented State Model for V_K(t)	p. 74
Braids and the Jones Polynomial	p. 85
Abstract Tensors and the Yang-Baxter Equation	p. 104
Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)_q	p. 117
The Form of the Universal R-matrix	p. 148
Yang-Baxter Models for Specializations of the Homily Polynomial	p. 161
The Alexander Polynomial	p. 174
Knot-Crystals - Classical Knot Theory in a Modern Guise	p. 186
The Kauffman Polynomial	p. 215
Oriented Models and Piecewise Linear Models	p. 235
Three Manifold Invariants from the Jones Polynomial	p. 250
Integral Heuristics and Witten's Invariants	p. 285
Appendix - Solutions to the Yang-Baxter Equation	p. 316
Knots and Physics - Miscellany
Theory of Hitches	p. 323
The Rubber Band and Twisted Tube	p. 329
On a Crossing	p. 332
Slide Equivalence	p. 336
Unoriented Diagrams and Linking Numbers	p. 339
The Penrose Chromatic Recursion	p. 346
The Chromatic Polynomial	p. 353
The Potts Model and the Dichromatic Polynomial	p. 364
Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum	p. 381
Quaternions, Cayley Numbers and the Belt Trick	p. 403
The Quaternion Demonstrator	p. 427
The Penrose Theory of Spin Networks	p. 443
Q-Spin Networks and the Magic Weave	p. 459
Knots and Strings - Knotted Strings	p. 475
DNA and Quantum Field Theory	p. 488
Knots in Dynamical Systems - The Lorenz Attractor	p. 501
Coda	p. 511
References	p. 513
Appendix
Introduction	p. 533
Gauss Codes, Quantum Groups and Ribbon Hopf Algebras	p. 543
Spin Networks, Topology and Discrete Physics	p. 589
Link Polynomials and a Graphical Calculus	p. 630
Knots, Tangles, and Electrical Networks	p. 676
Knot Theory and Functional Integration	p. 716
Introduction to Virtual Knot Theory and Khovanov Homology	p. 763
Index	p. 835
Table of Contents provided by Ingram. All Rights Reserved.

Knots And Physics (Fourth Edition)

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Paperback

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You Can Find This Book In

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