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Knots And Physics (Fourth Edition) 4th Revised edition [Kõva köide]

(Univ Of Illinois At Chicago, Usa)
  • Formaat: Hardback, 864 pages, illustrations
  • Sari: Series on Knots & Everything 53
  • Ilmumisaeg: 15-Jan-2013
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9814383007
  • ISBN-13: 9789814383004
Teised raamatud teemal:
  • Formaat: Hardback, 864 pages, illustrations
  • Sari: Series on Knots & Everything 53
  • Ilmumisaeg: 15-Jan-2013
  • Kirjastus: World Scientific Publishing Co Pte Ltd
  • ISBN-10: 9814383007
  • ISBN-13: 9789814383004
Teised raamatud teemal:
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 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.
Preface to the First Edition vii
Preface to the Second Edition xi
Preface to the Third Edition xiii
Preface to the Fourth Edition xv
Part I A Short Course of Knots and Physics
1 Physical Knots
4(4)
2 Diagrams and Moves
8(17)
3 States and the Bracket Polynomial
25(14)
4 Alternating Links and Checkerboard Surfaces
39(10)
5 The Jones Polynomial and its Generalizations
49(25)
6 An Oriented State Model for VK (t)
74(11)
7 Braids and the Jones Polynomial
85(19)
8 Abstract Tensors and the Yang-Baxter Equation
104(13)
9 Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q
117(31)
10 The Form of the Universal R-matrix
148(13)
11 Yang-Baxter Models for Specializations of the Homfly Polynomial
161(13)
12 The Alexander Polynomial
174(12)
13 Knot-Crystals - Classical Knot Theory in a Modern Guise
186(29)
14 The Kauffman Polynomial
215(20)
15 Oriented Models and Piecewise Linear Models
235(15)
16 Three Manifold Invariants from the Jones Polynomial
250(35)
17 Integral Heuristics and Witten's Invariants
285(31)
18 Appendix - Solutions to the Yang-Baxter Equation
316(7)
Part II Knots and Physics --- Miscellany
1 Theory of Hitches
323(6)
2 The Rubber Band and Twisted Tube
329(3)
3 On a Crossing
332(4)
4 Slide Equivalence
336(3)
5 Unoriented Diagrams and Linking Numbers
339(7)
6 The Penrose Chromatic Recursion
346(7)
7 The Chromatic Polynomial
353(11)
8 The Potts Model and the Dichromatic Polynomial
364(17)
9 Preliminaries for Quantum Mechanics, Spin Networks and Angular Momentum
381(22)
10 Quaternions, Cayley Numbers and the Belt Trick
403(24)
11 The Quaternion Demonstrator
427(16)
12 The Penrose Theory of Spin Networks
443(16)
13 Q-Spin Networks and the Magic Weave
459(16)
14 Knots and Strings - Knotted Strings
475(13)
15 DNA and Quantum Field Theory
488(13)
16 Knots in Dynamical Systems - The Lorenz Attractor
501(32)
Coda
511(2)
References
513(20)
Appendix
Introduction
533(10)
Gauss Codes, Quantum Groups and Ribbon Hopf Algebras
543(46)
Spin Networks, Topology and Discrete Physics
589(41)
Link Polynomials and a Graphical Calculus
630(46)
P. Vogel
Knots, Tangles, and Electrical Networks
676(40)
J. R. Goldman
Knot Theory and Functional Integration
716(47)
Introduction to Virtual Knot Theory and Khovanov Homology
763(72)
Index 835