The Interface Of Knots And Physics
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The Interface Of Knots And Physics
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Author : Louis H. Kauffman
language : en
Publisher: American Mathematical Soc.
Release Date : 1996
The Interface Of Knots And Physics written by Louis H. Kauffman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.
This text is the result of an AMS Short Course on Knots and Physics that was held in San Francisco in January 1994. The authors use ideas and methods of mathematical physics to extract topological information about knots and manifolds. The book features a basic introduction to knot polynomials in relation to statistical link invariants as well as concise introductions to topological quantum field theories and to the role of knot theory in quantum gravity.
The Interface Of Knots And Physics
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Author : Louis H. Kauffman
language : en
Publisher: American Mathematical Soc.
Release Date : 1995-12-01
The Interface Of Knots And Physics written by Louis H. Kauffman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995-12-01 with Knot theory categories.
This book is the result of an AMS Short Course on Knots and Physics that was held in San Francisco (January 1994). The range of the course went beyond knots to the study of invariants of low dimensional manifolds and extensions of this work to four manifolds and to higher dimensions. The authors use ideas and methods of mathematical physics to extract topological information about knots and manifolds. Features: A basic introduction to knot polynomials in relation to statistical link invariants. Concise introductions to topological quantum field theories and to the role of knot theory in quantum gravity. Knots and Physics would be an excellent supplement to a course on algebraic topology or a physics course on field theory.
The Interface Of Knots And Physics
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Author : Louis H. Kauffman
language : en
Publisher: American Mathematical Society(RI)
Release Date : 2014-05-10
The Interface Of Knots And Physics written by Louis H. Kauffman and has been published by American Mathematical Society(RI) this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with SCIENCE categories.
This text is the result of an AMS Short Course on Knots and Physics that was held in San Francisco in January 1994. The authors use ideas and methods of mathematical physics to extract topological information about knots and manifolds. The book features a basic introduction to knot polynomials in relation to statistical link invariants as well as concise introductions to topological quantum field theories and to the role of knot theory in quantum gravity.
Knots And Feynman Diagrams
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Author : Dirk Kreimer
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-20
Knots And Feynman Diagrams written by Dirk Kreimer and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-07-20 with Mathematics categories.
This volume explains how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. The author emphasizes how new discoveries in mathematics have inspired conventional calculational methods for perturbative quantum field theory to become more elegant and potentially more powerful methods. The material illustrates what may possibly be the most productive interface between mathematics and physics. As a result, it will be of interest to graduate students and researchers in theoretical and particle physics as well as mathematics.
Interface Of Knots And Physics
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Author : University of Illinois Staff
language : en
Publisher:
Release Date : 2000-08
Interface Of Knots And Physics written by University of Illinois Staff and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-08 with categories.
Tying Light In Knots
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Author : David S Simon
language : en
Publisher: Morgan & Claypool Publishers
Release Date : 2018-11-06
Tying Light In Knots written by David S Simon and has been published by Morgan & Claypool Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-06 with Science categories.
Topology is the study of properties of geometrical objects that remain invariant as the object is bent, twisted, or otherwise continuously deformed. It has been an indispensable tool in particle physics and solid state physics for decades, but in recent years it has become increasingly relevant in classical and quantum optics as well. It makes appearances through such diverse phenomena as Pancharatnam-Berry phases, optical vortices and solitons, and optical simulations of solid-state topological phenomena. This book concisely provides the necessary mathematical background needed to understand these developments and to give a rapid survey of some of the optical applications where topological issues arise.
A Gentle Introduction To Knots Links And Braids
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Author : Ruben Aldrovandi
language : en
Publisher: World Scientific
Release Date : 2021-10-14
A Gentle Introduction To Knots Links And Braids written by Ruben Aldrovandi and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-10-14 with Science categories.
The interface between Physics and Mathematics has been increasingly spotlighted by the discovery of algebraic, geometric, and topological properties in physical phenomena. A profound example is the relation of noncommutative geometry, arising from algebras in mathematics, to the so-called quantum groups in the physical viewpoint. Two apparently unrelated puzzles — the solubility of some lattice models in statistical mechanics and the integrability of differential equations for special problems — are encoded in a common algebraic condition, the Yang-Baxter equation. This backdrop motivates the subject of this book, which reveals Knot Theory as a highly intuitive formalism that is intimately connected to Quantum Field Theory and serves as a basis to String Theory.This book presents a didactic approach to knots, braids, links, and polynomial invariants which are powerful and developing techniques that rise up to the challenges in String Theory, Quantum Field Theory, and Statistical Physics. It introduces readers to Knot Theory and its applications through formal and practical (computational) methods, with clarity, completeness, and minimal demand of requisite knowledge on the subject. As a result, advanced undergraduates in Physics, Mathematics, or Engineering, will find this book an excellent and self-contained guide to the algebraic, geometric, and topological tools for advanced studies in theoretical physics and mathematics.
Energy Of Knots And Conformal Geometry
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Author : Jun O'Hara
language : en
Publisher: World Scientific
Release Date : 2003
Energy Of Knots And Conformal Geometry written by Jun O'Hara and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.
Energy of knots is a theory that was introduced to create a OC canonical configurationOCO of a knot OCo a beautiful knot which represents its knot type. This book introduces several kinds of energies, and studies the problem of whether or not there is a OC canonical configurationOCO of a knot in each knot type. It also considers this problems in the context of conformal geometry. The energies presented in the book are defined geometrically. They measure the complexity of embeddings and have applications to physical knotting and unknotting through numerical experiments. Contents: In Search of the OC Optimal EmbeddingOCO of a Knot: -Energy Functional E (); On E (2); L p Norm Energy with Higher Index; Numerical Experiments; Stereo Pictures of E (2) Minimizers; Energy of Knots in a Riemannian Manifold; Physical Knot Energies; Energy of Knots from a Conformal Geometric Viewpoint: Preparation from Conformal Geometry; The Space of Non-Trivial Spheres of a Knot; The Infinitesimal Cross Ratio; The Conformal Sin Energy E sin (c) Measure of Non-Trivial Spheres; Appendices: Generalization of the Gauss Formula for the Linking Number; The 3-Tuple Map to the Set of Circles in S 3; Conformal Moduli of a Solid Torus; Kirchhoff Elastica; Open Problems and Dreams. Readership: Graduate students and researchers in geometry & topology and numerical & computational mathematics."
Ideal Knots
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Author : A. Stasiak
language : en
Publisher: World Scientific
Release Date : 1998
Ideal Knots written by A. Stasiak and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Crafts & Hobbies categories.
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.
Knot Theory And Its Applications
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Author : Krishnendu Gongopadhyay
language : en
Publisher: American Mathematical Soc.
Release Date : 2016-09-21
Knot Theory And Its Applications written by Krishnendu Gongopadhyay and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-09-21 with Mathematics categories.
This volume contains the proceedings of the ICTS program Knot Theory and Its Applications (KTH-2013), held from December 10–20, 2013, at IISER Mohali, India. The meeting focused on the broad area of knot theory and its interaction with other disciplines of theoretical science. The program was divided into two parts. The first part was a week-long advanced school which consisted of minicourses. The second part was a discussion meeting that was meant to connect the school to the modern research areas. This volume consists of lecture notes on the topics of the advanced school, as well as surveys and research papers on current topics that connect the lecture notes with cutting-edge research in the broad area of knot theory.