Knots and physics
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 acc…
Read More ↓Title Statements
- Full title :Knots and physics / Louis H. Kauffman.
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.
Read More ↓Edition Statements
- Publication Date:2013.
- Edition:4th ed
Publication Statements
- Publisher(s):World Scientific
- Place of Publication:Hackensack, N.J
- Language:eng
- Publication Date:2013.
Notes
Description based upon print version of record.
5. TOPOLOGY: MIRROR IMAGES, TANGLES AND CONTINUED FRACTIONS
The Physical Object
- Description:1 online resource (865 p.).
Edition Identifiers
- ISBN:9814383023, 9789814383028, 1299133053, 9781299133051
- oclc:on1162511772
- LC Classification:QC20.7.K56
- Dewey Decimal:514
Table of 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 Linki…
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