Series on Knots and Everything - Vol. 1: Knots and Physics, Third Edition (Softcover)

Condition

VERY GOOD: The book is in very good condition, showing very little sign of use and wear.
NOTE: Some British spelling.

Product Details

From the back cover: "This invaluable book is an introduction to knot and link invariants as generatised 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. ...

"In this third edition, a paper by the author entitled 'Knot Theory and Functional Integration' has been added. This paper shows how the Kontsevich integral approach to the Vassiliev invariants is directly related to the perturbative expansion of Witten's functional integral. While the book supplies the background, this paper can be read interdependently as an introduction to quantum field theory and knot invariants and their relation to quantum gravity. As in the second edition there is a selection of papers by the author at the end of the book. Numerous clarifying remarks have been added to the book."

BRIEF CONTENTS

• 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 V_K(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 Homfly Polynomial
12. The 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 Recursive
7. the Chromatic Polynomial
8. The Potts Model and the Dichromatic 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

End Matter

• 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
• Link Polynomials and a Graphical Calculus (with P. Vogel)
• Knots, Tangles, and Electrical Networks (with J. R. Goldman)
• Knot Theory and Functional Integration