Knots And Physics Third Edition

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Knots And Physics

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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 2001

Knots And Physics written by Louis H. Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001 with Mathematics categories.

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.

Knots And Physics

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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 2013

Knots And Physics written by Louis H. Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.

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 Mathematics Of Knots

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Author : Markus Banagl
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-11-25

The Mathematics Of Knots written by Markus Banagl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-11-25 with Mathematics categories.

The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.

Knots And Physics

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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 1991

Knots And Physics written by Louis H. Kauffman and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.

This book is an introductory explication on the theme of knot and link invariants as generalized amplitudes (vacuum-vacuum amplitudes) for a quasi-physical process. The demands of the knot theory, coupled with a quantum statistical frame work create a context that naturally and powerfully includes an extraordinary range of interelated topics in topology and mathematical physics. The author takes a primarily combinatorial stance toward the 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 with and sometimes based on Part I. Part II also explores some side-topics such as frictional properties of knots, relations with combinatorics, knots in dynamical systems.

The Knot Book

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Author : Colin Conrad Adams
language : en
Publisher: American Mathematical Soc.
Release Date : 2004

The Knot Book written by Colin Conrad Adams 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 2004 with Mathematics categories.

Knots are familiar objects. Yet the mathematical theory of knots quickly leads to deep results in topology and geometry. This work offers an introduction to this theory, starting with our understanding of knots. It presents the applications of knot theory to modern chemistry, biology and physics.

Knots Braids And Mobius Strips Particle Physics And The Geometry Of Elementarity An Alternative View

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Author : Jack Shulman Avrin
language : en
Publisher: World Scientific
Release Date : 2015-03-13

Knots Braids And Mobius Strips Particle Physics And The Geometry Of Elementarity An Alternative View written by Jack Shulman Avrin and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-03-13 with Mathematics categories.

Elementary particles in this book exist as Solitons in-and-of the fabric of spacetime itself. As such they are characterized by their geometry, that is their topology and configuration which lead directly to their physical attributes and behavior as well as to a simplification and reduction of assumptions and the importation of parameter values. The emphasis of the book is thus on that geometry, the algebraic geometry associated with taxonomical issues and the differential geometry that determines the physics as well as on simplifying the results. In itself, however, the process of assembling and developing what eventually went into the book has been a singularly rewarding journey. Along the way some fascinating insights and connections to known physical attributes and theories emerge, some predictable but others unbidden and even unanticipated. The book is intended to summarize that journey in a way that, readers with a range of backgrounds will find interesting and provocative. Connections to other physical theories and subjects are also discussed. A most gratifying development is the emergence of a unifying principle underlying the epistemological structure of not only the elementary particles but of such diverse fields as Radar, Quantum mechanics, Biology, Cosmology and the Philosophy of science.

Volume Conjecture For Knots

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Author : Hitoshi Murakami
language : en
Publisher: Springer
Release Date : 2018-08-15

Volume Conjecture For Knots written by Hitoshi Murakami and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-08-15 with Science categories.

The volume conjecture states that a certain limit of the colored Jones polynomial of a knot in the three-dimensional sphere would give the volume of the knot complement. Here the colored Jones polynomial is a generalization of the celebrated Jones polynomial and is defined by using a so-called R-matrix that is associated with the N-dimensional representation of the Lie algebra sl(2;C). The volume conjecture was first stated by R. Kashaev in terms of his own invariant defined by using the quantum dilogarithm. Later H. Murakami and J. Murakami proved that Kashaev’s invariant is nothing but the N-dimensional colored Jones polynomial evaluated at the Nth root of unity. Then the volume conjecture turns out to be a conjecture that relates an algebraic object, the colored Jones polynomial, with a geometric object, the volume. In this book we start with the definition of the colored Jones polynomial by using braid presentations of knots. Then we state the volume conjecture and give a very elementary proof of the conjecture for the figure-eight knot following T. Ekholm. We then give a rough idea of the “proof”, that is, we show why we think the conjecture is true at least in the case of hyperbolic knots by showing how the summation formula for the colored Jones polynomial “looks like” the hyperbolicity equations of the knot complement. We also describe a generalization of the volume conjecture that corresponds to a deformation of the complete hyperbolic structure of a knot complement. This generalization would relate the colored Jones polynomial of a knot to the volume and the Chern–Simons invariant of a certain representation of the fundamental group of the knot complement to the Lie group SL(2;C). We finish by mentioning further generalizations of the volume conjecture.

Linknot

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Author : Slavik V. Jablan
language : en
Publisher: World Scientific
Release Date : 2007

Linknot written by Slavik V. Jablan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.

LinKnot OCo Knot Theory by Computer provides a unique view of selected topics in knot theory suitable for students, research mathematicians, and readers with backgrounds in other exact sciences, including chemistry, molecular biology and physics. The book covers basic notions in knot theory, as well as new methods for handling open problems such as unknotting number, braid family representatives, invertibility, amphicheirality, undetectability, non-algebraic tangles, polyhedral links, and (2,2)-moves. Hands-on computations using Mathematica or the webMathematica package LinKnot (available online at http: //math.ict.edu.rs ) and beautiful illustrations facilitate better learning and understanding. LinKnot is also a powerful research tool for experimental mathematics implementation of Caudron's ideas. The use of Conway notation enables experimenting with large families of knots and links. Conjectures discussed in the book are explained at length. The beauty, universality and diversity of knot theory is illuminated through various non-standard applications: mirror curves, fullerens, self-referential systems, and KL automata. Sample Chapter(s). 1.1 Basic graph theory (176 KB). Contents: Notation of Knots and Links; Recognition and Generation of Knots and Links; History of Knot Theory and Applications of Knots and Links. Readership: Researchers interested in knot theory and users of Mathematica."

The Self Evolving Cosmos

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Author : Steven M. Rosen
language : en
Publisher: World Scientific
Release Date : 2008

The Self Evolving Cosmos written by Steven M. Rosen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Science categories.

This unique book offers an original way of thinking about two of the most significant problems confronting modern theoretical physics: the unification of the forces of nature and the evolution of the universe. In bringing out the inadequacies of the prevailing approach to these questions, the author demonstrates the need for more than just a new theory. The meanings of space and time themselves must be radically rethought, which requires a whole new philosophical foundation. To this end, the book turns to the phenomenological writings of Maurice Merleau-Ponty and Martin Heidegger. Their insights into space and time bring the natural world to life in a manner well-suited to the dynamic phenomena of contemporary physics. In aligning continental thought with problems in physics and cosmology, the book makes use of topology . Phenomenological intuitions about space and time are systematically fleshed out via an unconventional and innovative approach to this qualitative branch of mathematics. The author''s pioneering work in topological phenomenology is applied to such topics as quantum gravity, cosmogony, symmetry, spin, vorticity, dimension theory, Kaluza-Klein and string theories, fermion-boson interrelatedness, hypernumbers, and the mind-matter interface. Sample Chapter(s). Chapter 1: Introduction Individuation and the Quest for Unity (77 KB). Contents: Introduction: Individuation and the Quest for Unity; The Obstacle to Unification in Modern Physics; The Phenomenological Challenge to the Classical Formula; Topological Phenomenology; The Dimensional Family of Topological Spinors; Basic Principles of Dimensional Transformation; Waves Carrying Waves: The Co-Evolution of Lifeworlds; The Forces of Nature; Cosmogony, Symmetry, and Phenomenological Intuition; The Self-Evolving Cosmos; The Psychophysics of Cosmogony. Readership: Philosophically-oriented readers drawn to current developments in physics and cosmology. For academics and scientists dealing with the foundations of physics, the philosophy of science in general, and or contemporary phenomenological thought.

Self Evolving Cosmos The A Phenomenological Approach To Nature S Unity In Diversity

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Author : Steven M Rosen
language : en
Publisher: World Scientific
Release Date : 2008-02-22

Self Evolving Cosmos The A Phenomenological Approach To Nature S Unity In Diversity written by Steven M Rosen and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-02-22 with Science categories.

This unique book offers an original way of thinking about two of the most significant problems confronting modern theoretical physics: the unification of the forces of nature and the evolution of the universe. In bringing out the inadequacies of the prevailing approach to these questions, the author demonstrates the need for more than just a new theory. The meanings of space and time themselves must be radically rethought, which requires a whole new philosophical foundation. To this end, the book turns to the phenomenological writings of Maurice Merleau-Ponty and Martin Heidegger. Their insights into space and time bring the natural world to life in a manner well-suited to the dynamic phenomena of contemporary physics.In aligning continental thought with problems in physics and cosmology, the book makes use of topology. Phenomenological intuitions about space and time are systematically fleshed out via an unconventional and innovative approach to this qualitative branch of mathematics. The author's pioneering work in topological phenomenology is applied to such topics as quantum gravity, cosmogony, symmetry, spin, vorticity, dimension theory, Kaluza-Klein and string theories, fermion-boson interrelatedness, hypernumbers, and the mind-matter interface.