Knots and physics / Louis H. Kauffman.

Format:

Book

Author/Creator:

Kauffman, Louis H.

Series:

K & E series on knots and everything ; v. 53.

Series on knots and everything ; v. 53

Language:

English

Subjects (All):

Knot polynomials.

Mathematical physics.

Physical Description:

1 online resource (865 p.)

Edition:

4th ed.

Place of Publication:

Hackensack, N.J. : World Scientific, 2013.

Language Note:

English

Summary:

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 i

Contents:

Preface to the First Edition; Preface to the Second Edition; Preface to the Third Edition; Preface to the Fourth Edition; Table of Contents; 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 S L(2}q

10. The Form of the Universal R-matrix11. 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 1\1be; 3. On a Crossing.; 4. Slide Equivalence

5. Unoriented Diagrams and Linking Numbers6. The Penrose Chromatic Recursion; 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 . . . . . . . . . . . . . 501 Coda; References; Appendix

IntroductionGauss Codes, Quantum Groups and Ribbon Hopf Algebras; I. Introduction; II. Knots and the Gauss Code; III. Jordan Curves and Immersed Plane Curves; IV. The Abstract Tensor Model for Link Invariants; V. From Abstract Tensors to Quantum Algebras; VI. From Quantum Algebra to Quantum Groups; VII. Categories; VIII. Invariants of 3-Manifolds; IX. Epilogue; References; Spin Networks, Topology and Discrete Physics; I. Introduction; II. Trees and Four Colors; III. The Temperley Lieb Algebra; IV. Temperley Lieb Recoupling Theory; V. Penrose Spin Networks; VI. Knots and 3-Manifolds

VII. The Shadow WorldVIII. The Invariants of Ooguri, Crane and Yetter; References; Link Polynomials and a Graphical Calculus (with P. Vogel}; 0. Introduction; 1. Rigid Vertex Isotopy; 2. The Homfty Polynomial; 3. Braids and the Heeke Algebra; 4. Demonstration of Identities in Oriented Graphical Calculus; 5. The Dubrovnik Polynomial; REFERENCES; Knots, Tangles, and Electrical Networks (with J. R. Goldman); CONTENTS; 1. INTRODUCTION; 2. KNOTS, TANGLES, AND GRAPHS; 3. CLASSICAL ELECTRICITY; 4. MODERN ELECTRICITY-THE CONDUCTANCE INVARIANT

5. TOPOLOGY: MIRROR IMAGES, TANGLES AND CONTINUED FRACTIONS

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

981-4383-02-3

1-299-13305-3

OCLC:

828792700