Knots and Physics

Knots and Physics

The Square Knot Figure 3 In Figure 3 we find the square knot, excellent for splicing two lengths of rope. Tension at A and B creates an effect of mutual constriction - keeping the knot from slipping. And finally in this rogue's gallery ...

Author: Louis H. Kauffman

Publisher: World Scientific

ISBN: 9789814383004

Category: Mathematics

Page: 846

View: 819

An introduction to knot and link invariants as generalised 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.
Categories: Mathematics

Knots and Physics

Knots and Physics

In Figure 3 we find the square knot, excellent for splicing two lengths of rope. Tension at A and B creates an effect of mutual constriction - keeping the knot from slipping. And finally in this rogue's gallery of knots and hitches we ...

Author: Louis H Kauffman

Publisher: World Scientific

ISBN: 9789814494090

Category: Mathematics

Page: 788

View: 268

This invaluable book is an introduction to knot and link invariants as generalised 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 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 independently 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 text. Contents:Physical KnotsStates and the Bracket PolynomialThe Jones Polynomial and Its GeneralizationsBraids and the Jones PolynomialFormal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)qYang-Baxter Models for Specializations of the Homfly PolynomialKnot-Crystals — Classical Knot Theory in a Modern GuiseThe Kauffman PolynomialThree Manifold Invariants from the Jones PolynomialIntegral Heuristics and Witten's InvariantsThe Chromatic PolynomialThe Potts Model and the Dichromatic PolynomialThe Penrose Theory of Spin NetworksKnots and Strings — Knotted StringsDNA and Quantum Field TheoryKnots in Dynamical Systems — The Lorenz Attractorand selected papers Readership: Physicists and mathematicians. Keywords:Knots;Kauffman;Jones PolynomialReviews: “It is an attractive book for physicists with profuse and often entertaining illustrations … proofs … seldom heavy and nearly always well explained with pictures … succeeds in infusing his own excitement and enthusiasm for these discoveries and their potential implications.” Physics Today “The exposition is clear and well illustrated with many examples. The book can be recommended to everyone interested in the connections between physics and topology of knots.” Mathematics Abstracts “… here is a gold mine where, with care and patience, one should get acquainted with a beautiful subject under the guidance of a most original and imaginative mind.” Mathematical Reviews
Categories: Mathematics

Knots and Physics

Knots and Physics

In Figure 3 we find the square knot, excellent for splicing two lengths of rope. Tension at A and B creates an effect of mutual constriction - keeping the knot from slipping. And finally in this rogue's gallery of knots and hitches we ...

Author: Louis H Kauffman

Publisher: World Scientific

ISBN: 9789814502375

Category: Science

Page: 740

View: 462

In this second edition, the following recent papers have been added: “Gauss Codes, Quantum Groups and Ribbon Hopf Algebras”, “Spin Networks, Topology and Discrete Physics”, “Link Polynomials and a Graphical Calculus” and “Knots Tangles and Electrical Networks”. An appendix with a discussion on invariants of embedded graphs and Vassiliev invariants has also been included. This book is an introduction to knot and link invariants as generalized amplitudes (vacuum–vacuum 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 has the advantage of providing very direct access to the algebra and to the combinatorial topology, as well as the physical ideas. This book is divided into 2 parts: Part I of the book is a systematic course in knots and physics starting from the ground up. Part II is a set of lectures on various topics related to and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics and knots in dynamical systems. Contents:Physical KnotsStates and the Bracket PolynomialThe Jones Polynomial and Its GeneralizationsBraids and the Jones PolynomialFormal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)qYang-Baxter Models for Specializations of the Homfly PolynomialThe Alexander PolynomialKnot-Crystals — Classical Knot Theory in Modern GuiseThe Kauffman PolynomialThree Manifold Invariants from the Jones PolynomialIntegral Heuristics and Witten' s InvariantsThe Chromatic PolynomialThe Potts Model and the Dichromatic PolynomialThe Penrose Theory of Spin NetworksKnots and Strings — Knotted StringsDNA and Quantum Field TheoryKnots in Dynamical Systems — The Lorenz Attractorand other papers Readership: Physicists, mathematical physicists and mathematicians. keywords: Reviews of the First Edition: “It is an attractive book for physicists with profuse and often entertaining illustrations … proofs … seldom heavy and nearly always well explained with pictures… succeeds in infusing his own excitement and enthusiasm for these discoveries and their potential implications.” Physics Today “… here is a gold mine where, with care and patience, one should get acquainted with a beautiful subject under the guidance of a most original and imaginative mind.” Mathematical Reviews
Categories: Science

The Knot Geometry journey Part II

The Knot Geometry journey   Part II

Introduction Part I 1 Knot Gallery p. 7 2 Knot Gallery log p. 61 p. 75 3 Knot Gallery references Part II 4 Knot Geometry p. 79 5 Knot Geometry log p. 133 p. 147 6 Knot Geometry references Part III 7 Knot Geometry Windmap journey p.

Author: Jean Constant

Publisher: Hermay NM

ISBN:

Category: Art

Page: 69

View: 934

Volume 12 of the Math-Art series. This 3-part book is a visual exploration of knot geometry and ethnomathematics to celebrate the similarities between abstract geometry and unique cultures worldwide. Starting at latitude 0º, longitude 0º, the author set sail (virtually) westward at an average of 400 (nautical) knots a week to fully cover its circumference and explore 1 new knot each week for an entire year. Part I is the art portfolio extracted from the geometry models, part II is a detailed record of the original geometry used to create the artwork, and part III is the weekly wind map log showing the project’s positioning, actual winds, and currents in real-time. Each book includes 52 illustrations, notes, and references.
Categories: Art

The Knot Geometry journey Part I

The Knot Geometry journey   Part I

Introduction Part I 1 Knot Gallery p. 7 2 Knot Gallery log p. 61 p. 75 3 Knot Gallery references Part II 4 Knot Geometry p. 79 5 Knot Geometry log p. 133 p. 147 6 Knot Geometry references Part III 7 Knot Geometry Windmap journey p.

Author: Jean Constant

Publisher: Hermay NM

ISBN:

Category: Art

Page: 83

View: 852

Volume 12 of the Math-Art series. This 3-part book is a visual exploration of knot geometry and ethnomathematics to celebrate the similarities between abstract geometry and unique cultures worldwide. Starting at latitude 0º, longitude 0º, the author set sail (virtually) westward at an average of 400 (nautical) knots a week to fully cover its circumference and explore 1 new knot each week for an entire year. Part I is the art portfolio extracted from the geometry models, part II is a detailed record of the original geometry used to create the artwork, and part III is the weekly wind map log showing the project’s positioning, actual winds, and currents in real-time. Each book includes 52 illustrations, notes, and references.
Categories: Art

The Knot Geometry journey Part III

The Knot Geometry journey   Part III

Introduction Part I 1 Knot Gallery p. 7 2 Knot Gallery log p. 61 p. 75 3 Knot Gallery references Part II 4 Knot Geometry p. 79 5 Knot Geometry log p. 133 p. 147 6 Knot Geometry references Part III 7 Knot Geometry Windmap journey p.

Author: Jean Constant

Publisher: Hermay NM

ISBN:

Category: Art

Page: 22

View: 631

Volume 12 of the Math-Art series. This 3-part book is a visual exploration of knot geometry and ethnomathematics to celebrate the similarities between abstract geometry and unique cultures worldwide. Starting at latitude 0º, longitude 0º, the author set sail (virtually) westward at an average of 400 (nautical) knots a week to fully cover its circumference and explore 1 new knot each week for an entire year. Part I is the art portfolio extracted from the geometry models, part II is a detailed record of the original geometry used to create the artwork, and part III is the weekly wind map log showing the project’s positioning, actual winds, and currents in real-time. Each book includes 52 illustrations, notes, and references.
Categories: Art

Ideal Knots

Ideal Knots

Finally, given two tangled configurations, we would like to be able to establish if they represent a knot of the same ... Figure 1: Knot gallery: a) unknot b) left trefoil c) right trefoil d) figure eight knot e) star knot f) a knot ...

Author: A. Stasiak

Publisher: World Scientific

ISBN: 9789812796073

Category: Crafts & Hobbies

Page: 424

View: 517

In this book, experts in different fields of mathematics, physics, chemistry and biology present unique forms of knots which satisfy certain preassigned criteria relevant to a given field. They discuss the shapes of knotted magnetic flux lines, the forms of knotted arrangements of bistable chemical systems, the trajectories of knotted solitons, and the shapes of knots which can be tied using the shortest piece of elastic rope with a constant diameter.
Categories: Crafts & Hobbies

The Nail Knot

The Nail Knot

Gallery Books An Imprint of Simon & Schuster, Inc. 1230 Avenue of the Americas New York, NY 10020 www.SimonandSchuster.com This book is a work of ction. Any references to historical events, real people, or real places are used ...

Author: John Galligan

Publisher: Simon and Schuster

ISBN: 9781440532412

Category: Fiction

Page: 231

View: 207

The going has gotten tough, and Ned ''Dog'' Oglivie has gone fishing. Fly fishing. For trout. All across America. At least until his money runs out . . . Driven by tragedy to turn his back on human society, the Dog is on a quest to fish himself into oblivion. And he's nearly made it. Playing the back highways of America in a wounded old RV . . . provisioned with a supply of peanut butter sandwiches, bad cigars, and vodka-Tang . . . armed with a loaded pistol (for when the money runs out) . . . the Dog is nearly at the end of his tether when he rolls into little Black Earth, Wisconsin, intending to fish the yellow sally stonefly hatch . . . and finds a body instead. Who killed Jake Jacobs, fellow fly fisher and late-coming agitator who was trying to save Black Earth Creek? Why was Jacobs disfigured in such a peculiar way? Why does the Dog give a damn? Can he rekindle his faith and interest in humankind? By caring about the death of a stranger, can the Dog recover his own life? Can he untie The Nail Knot?
Categories: Fiction

The Knot Complete Guide to Weddings

The Knot Complete Guide to Weddings

REAL BRIDE ADVICE capturing your day “Do a first-look and get photos with your groom before the ceremony. It gave us more time for photos with our family and made our day run smoothly. Our couple shots were great, and walking down the ...

Author: Carley Roney

Publisher: Potter Style

ISBN: 9780770433390

Category: Reference

Page: 448

View: 625

From the #1 wedding website, this completely revised and updated edition of the classic wedding planning bible answers all of your questions, with all the latest information and tools a bride could want. Overwhelmed by the countless questions and details your wedding entails? Don't despair! The Knot Complete Guide to Weddings takes you step-by-step from your engagement to the big day, from the reception to the honeymoon. Inside you'll find checklists, worksheets, insider advice, and in-depth sections on: • How to personalize your wedding • Updated wedding etiquette • Creating a realistic budget • Sneaky cost-cutting tips • Dress shopping advice • Tips for working with florists, caterers, officiants, and others • Invitation wording • Vows and ceremony details • Unique Wedding customs Plus, all new sections on: Planning Online and Destination Weddings, and a color-coded section with over 100 vibrant photographs.
Categories: Reference

A hard knot

A hard knot

Pictures at South Kensington . With 70 Illustrations . 18 . The English Pictures at the National Gallery . 114 Illustrations . ls . The Old Masters at the National Gallery . 128 Illustrations . ls . 6d . A Complete Illustrated Catalogue ...

Author: Charles Gibbon

Publisher:

ISBN: OXFORD:555044495

Category:

Page:

View: 244

Categories: