Knots and physics

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Title 
Knots and physics 
Creator 
Kauffman, Louis H., 1945 
Contributors 
World Scientific (Firm) 
DescriptionAbstract 
This invaluable book is an introduction to knot and link invariants as generalized amplitudes for a quasiphysical process. The demands of knot theory, coupled with a quantumstatistical 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 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. In this new edition, articles on other topics, including Khovanov Homology, have been included. 
DescriptionTable Of Contents 
pt. 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 YangBaxter equation. 9. Formal Feynman diagrams, bracket as a vacuumvacuum expectation and the quantum group SL(2)q. 10. The form of the universal Rmatrix. 11. YangBaxter models for specializations of the Homfly polynomial. 12. The Alexander polynomial. 13. Knotcrystals  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 YangBaxter equation  pt. 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 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. Qspin networks and the magic wave. 14. Knots and strings  knotted strings. 15. DNA and quantum field theory. 16. Knots in dynamical systems  the Leronz attractor 
Publisher 
World Scientific Pub. Co. 
Subject 
Knot polynomials. Mathematical physics. 
Identifier (Full text) 
9789814383028 (electronic bk.) ; 9789814383004 ; 9789814383011 (pbk.) ; http://www.worldscientific.com/worldscibooks/10.1142/8338#t=toc 
Language 
eng 
Type 
Electronic books. 
FormatExtent 
xviii, 846 p. : ill. 
Date 
c2013. 
RelationIs Part Of 
K & E series on knots and everything v. 53 
OCLC number 
874498081 
CONTENTdm number 
409 
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