2 edition of **Braid Group Knot Theory and Statistical Mechanics (Advanced Series in Mathematical Physics, Vol 9)** found in the catalog.

Braid Group Knot Theory and Statistical Mechanics (Advanced Series in Mathematical Physics, Vol 9)

M. L. Ge

- 69 Want to read
- 16 Currently reading

Published
**March 1989**
by World Scientific Pub Co Inc
.

Written in English

- Statistical physics,
- General,
- Mathematics

**Edition Notes**

Contributions | C. N. Yang (Editor) |

The Physical Object | |
---|---|

Format | Paperback |

Number of Pages | 336 |

ID Numbers | |

Open Library | OL9712500M |

ISBN 10 | 9971508338 |

ISBN 10 | 9789971508333 |

A general theory is presented to construct representations of the braid group and link polynomials (topological invariants for knots and links) from exactly solvable models in statistical mechanics at criticality. Sufficient conditions for the existence of the Markov trace are explicitly shown. The reader is referred to [14, 26, 27, 28–31, 33–35, 44–47] for more information on relationships of knot theory with statistical mechanics, Hopf algebras and quantum groups. For topology, the key point is that Lie algebras can be used to construct invariants of knots and by:

If you would have asked about a particular department I would have suggested you books of that department. As you have not specified the department I will provide provide books of major departments of physics: 1. M.S. Longair: Theoretical concept. Yang, Ge (eds.), Braid Group, Knot Theory and Statistical Mechanics (unfree) Yang, Ge (eds.), Braid Group, Knot Theory and Statistical Mechanics II (unfree) Yeomans, Statistical Mechanics of Phase Transitions (unfree) Yoshioka, Statistical Physics, An Introduction (unfree).

In this pap er we will study how knot theory can b e used to pro duce unitary representations of the braid group. Such represen tations can play a fundamen tal role in quantum computing. K. Reidemeister in By , knot theory had become a well-developed area of topology [7]. The discovery of the Jones polynomial by Vaughan Jones in not only showed a connection between knot theory and di erent areas of mathemat-ics (operator algebras, braid theory, quantum groups), but also to physics (statistical models) [2], [8].

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Then in the 's Vaughn Jones discovered some invariants that are related to ideas in physics, namely the theory of integrable models in statistical mechanics. This book is a collection of articles discussing the Jones work and other approaches that relate knot theory and statistical mechanics, written a few years after his by: The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics.

This book is based on the volume but has new material included and new contributors. Contents: On the Combinatorics of Vassiliev Invariants (J S Birman). Then in the 's Vaughn Jones discovered some invariants that are related to ideas in physics, namely the theory of integrable models in statistical mechanics.

This book is a collection of articles discussing the Jones work and other approaches that relate knot theory and statistical mechanics, written a few years after his discovery.4/5(1). Notes on Subfactors and Statistical Mechanics (V F R Jones) Polynomial Invariants in Knot Theory (L H Kauffman) Algebras of Loops on Surfaces, Algebras of Knots, and Quantization (V G Turaev) Quantum Groups (L Faddeev et al.) Introduction to the Yang-Baxter Equation (M Jimbo) Integrable Systems Related to Braid Groups and Yang-Baxter Equation.

ISBN: OCLC Number: Description: vii, pages: illustrations ; 23 cm. Contents: Notes on subfactors and statistical mechanics / V.F.R. Jones --Polynomial invariants in knot theory / Louis H.

Kauffman --Algebras of loops on surfaces, algebras of knots, and quantization / V.G. Turaev --Quantum groups / L. Faddeev, N. Reshetikhin and. Get this from a library. Braid group, knot theory, and statistical mechanics II. [Chen Ning Yang; M L Ge;] -- The present volume is an updated version of the book edited by C.N.

Yang and M.L. Ge on the topics of braid groups and knot theory, which are related to statistical mechanics. This book is based on. Knot TheoryKnot Theory and Statistical Mechanics.

KNOTS: A 3-dimensional loop projected onto a Example of converting a knot into a braid Braid group:Braid group: Knot invariants and statistical mechanicsKnot invariants and statistical mechanics V.

Jones, Pacific J. Math. 17 () File Size: 2MB. Braid Group, Knot Theory and Statistical Mechanics II 作者: C. Yang 出版社: World Scientific Pub Co Inc 出版年: 页数: 定价: USD 装帧: Hardcover ISBN: A quite easy book on the links with Knot Theory is.

Prasolov, Sossinsky - Knots, Links, Braids and 3-Manifolds, Translations of Mathematical MonographsAmerican Mathematical Society. but, really, any textbook on Knot Theory worth its price will talk about braids at some point.

The present volume is an updated version of the book Editor C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics.

This book is based on the volume but has new material included and new. The present volume is an updated version of the book edited by C N Yang and M L Ge on the topics of braid groups and knot theory, which are related to statistical mechanics.

This book is based on the volume but has new material included and new contributors. In topology, knot theory is the study of mathematical inspired by knots which appear in daily life, such as those in shoelaces and rope, a mathematical knot differs in that the ends are joined together so that it cannot be undone, the simplest knot being a ring (or "unknot").In mathematical language, a knot is an embedding of a circle in 3-dimensional Euclidean space, R 3 (in.

Book: Braid Group, Knot Theory and Statistical Mechanics II (Advanced Series in Mathematical Physics) (v.2) Author: C. Yang Date: Pages: Format: djvu Language: English ISBN X Product Description: Dealing with the topics of braid groups and knot theory which are related to statistical mechanics, this updated edition is based upon the version.

Braid Group, Knot Theory and Statistical Mechanics (Advanced Series in Mathematical Physics) 作者: C. Yang 出版社: World Scientific Pub Co Inc 出版年: 定价: USD 装. Braid Group Knot Theory and Statistical Mechanics (Advanced Series in Mathematical Physics, Vol 9) by M. Ge Free PDF d0wnl0ad, audio books, books to read, good books to read, cheap books, good books, online books, books online, book reviews epub, read books online, books to read online, online library, greatbooks to read, PDF best books to.

begun to make contributions to knot theory. From aroundknot theory came to attention not only in almost all areas of mathematics, but also in the fields of science that will be cutting-edge researches, such as gene synthesis, quantum statistical mechanics, soft matter physics, biochemistry, polymer network, applied chemistry.

Then the Yang-Baxter equation shows that, But there are zillions of examples -- take a look at his book on exactly solvable statistical mechanics models. Yang and M. Ge, Braid Group, Knot Theory, and Statistical Mechanics, World Scientific, New Jersey, In the mathematical field of knot theory, the Jones polynomial is a knot polynomial discovered by Vaughan Jones in in statistical mechanics.

Let a link L be given. A theorem of Alexander states that it is the trace closure of a braid, say with n strands. The Knot Book. The reader is referred to [30,31,39,40,[44][45][46] [47] 56,75,76,79,80] for more information about relationships of knot theory with statistical mechanics, Hopf algebras and quantum groups.

For Author: Louis Kauffman. Read the latest articles of Advances in Mathematics atElsevier’s leading platform of peer-reviewed scholarly literature.

About C.N. Yang: Chen Ning Yang. C.N. Yang is the author of Braid Group, Knot Theory and Statistical Mechanics ( avg rating, 0 ratings, 0 reviews, p /5.Colin Adams’s The Knot Book is the first book to make cutting-edge research in knot theory The study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory.4/5.Braid theory weaves together entrepreneurs, industry influencers and corporate partners to accelerate adoption of transformative technology, drive market growth and create profitable collaborations.