纽结及物理KNOTS AND PHYSICS, THIRD EDITION
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作者： Louis H. Kauffman 著
出 版 社： Penguin
出版时间： 2001-12-1字数：版次： 1页数： 770印刷时间： 2001/12/01开本：印次： 1纸张： 胶版纸I S B N ： 9789810241124包装： 平装内容简介
This invaluable book is an introduction to knot and link invariants as generalised 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 thesesubjects. 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.
目录
Preface to the First Edition
Preface to the Second Edition
Preface to the Third Edition
Part I. A Short Course of Knots and Physics
1. Physical Knots
2. Diagrams and Moves
3. States and the Bracket Polynomial
4. Alternating Links and Checkerboard Surfaces
5. The Jones Polynomial and its Generalizations
6. An Oriented State Model for VK(t)
7. Braids and the Jones Polynomial
8. Abstract Tensors and the Yang-Baxter Equation
9. Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q
10. The Form of the Universal R-matrix
11. Yang-Baxter Models for Specializations of the Homily Polynomial ..
12. Tile Alexander Polynomial
13. Knot-Crystals - Classical Knot Theory in a Modern Guise
14. The Kauffman Polynomial
15. Oriented Models and Piecewise Linear Models
16. Three Manifold Invariants from the Jones Polynomial
17. Integral Heuristics and Witten's Invariants
18. Appendix - Solutions to the Yang-Baxter Equation
Part II. Knots and Physics-Miscellany
1. Theory of Hitches
2. The Rubber Band and Twisted Tube
3. On a Crossing
4. Slide Equivalence
5. Unoriented Diagrams and Linking Numbers
6. The Penrose Chromatic Recursion
7. The Chromatic Polynomial
8. The Potts Model and the Dichrornatic Polynomial
9. Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum
10. Quaternions, Cayley Numbers and the Belt Trick
11. The Quaternion Demonstrator
12. The Penrose Theory of Spin Networks
13. Q-Spin Networks and the Magic Weave
14. Knots and Strings - Knotted Strings
15. DNA and Quantum Field Theory
16. Knots in Dynamical Systems - The Lorenz Attractor
Coda
References
Index
Appendix
Introduction
Gauss Codes, Quantum Groups and Ribbon Hopf Algebras
Spin Networks, Topology and Discrete Physics
Link Polynomials and a Graphical Calculus
Knots, Tangles, and Electrical Networks
Knot Theory and Functional Integration
