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Tables of Contents for Knots and Physics
Chapter/Section Title
Page #
Page Count
Preface to the First Edition
vii
Preface to the Second Edition
xi
Preface to the Third Edition
xiii
Part I. A Short Course of Knots and Physics
Physical Knots
4
4
Diagrams and Moves
8
17
States and the Bracket Polynomial
25
14
Alternating Links and Checkerboard Surfaces
39
10
The Jones Polynomial and its Generalizations
49
25
An Oriented State Model for VK(t)
74
11
Braids and the Jones Polynomial
85
19
Abstract Tensors and the Yang-Baxter Equation
104
13
Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q
117
31
The Form of the Universal R-Matrix
148
13
Yang-Baxter Models for Specializations of the Homfly Polynomial
161
13
The Alexander Polynomial
174
12
Knot-Crystals --- Classical Knot Theory in a Modern Guise
186
29
The Kauffman Polynomial
215
20
Oriented Models and Piecewise Linear Models
235
15
Three Manifold Invariants from the Jones Polynomial
250
35
Integral Heuristics and Witten's Invariants
285
31
Appendix -- Solutions to the Yang-Baxter Equation
316
7
Part II. Knots and Physics --- Miscellany
Theory of Hitches
323
6
The Rubber Band and Twisted Tube
329
3
On a Crossing
332
4
Slide Equivalence
336
3
Unoriented Diagrams and Linking Numbers
339
7
The Penrose Chromatic Recursion
346
7
The Chromatic Polynomial
353
11
The Potts Model and the Dichromatic Polynomial
364
17
Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum
381
22
Quaternions, Cayley Numbers and the Belt Trick
403
24
The Quaternion Demonstrator
427
16
The Penrose Theory of Spin Networks
443
16
Q-Spin Networks and the Magic Weave
459
16
Knots and Strings --- Knotted Strings
475
13
DNA and Quantum Field Theory
488
13
Knots in Dynamical Systems --- The Lorenz Attractor
501
10
Coda
511
2
References
513
18
Index
531
10
Appendix
Introduction
541
10
Gauss Codes, Quantum Groups and Ribbon Hopf Algebras
551
46
Spin Networks, Topology and Discrete Physics
597
41
Link Polynomials and a Graphical Calculus
638
46
P. Vogel
Knots, Tangles, and Electrical Networks
684
40
J. R. Goldman
Knot Theory and Functional Integration
724