Knots And Quantum Gravity
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Knots And Quantum Gravity
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Author : John C. Baez
language : en
Publisher:
Release Date : 2023
Knots And Quantum Gravity written by John C. Baez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023 with Gauge fields (Physics) categories.
The discovery of relations between quantum gravity and the theory of knots and links came as a surprise, since the topics had been regarded as quite remote from each other. This volume contains the proceedings of a workshop designed to bring together researchers in knot theory and quantum gravity.
Loops Knots Gauge Theories And Quantum Gravity
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Author : Rodolfo Gambini
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-03
Loops Knots Gauge Theories And Quantum Gravity written by Rodolfo Gambini 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 2000-07-03 with Mathematics categories.
Now in paperback, this text provides a self-contained introduction to applications of loop representations and knot theory in particle physics and quantum gravity. Loop representations (and the related topic of knot theory) are of considerable current interest because they provide a unified arena for the study of the gauge invariant quantization of Yang-Mills theories and gravity, and suggest a promising approach to the eventual unification of the four fundamental forces. This text begins with a detailed review of loop representation theory. It then goes on to describe loop representations in Maxwell theory, Yang-Mills theories as well as lattice techniques. Applications in quantum gravity are then discussed in detail. Following chapters move on to consider knot theories, braid theories and extended loop representations in quantum gravity. A final chapter assesses the current status of the theory and points out possible directions for future research.
Gauge Fields Knots And Gravity
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Author : John Baez
language : en
Publisher: World Scientific Publishing Company
Release Date : 1994-10-24
Gauge Fields Knots And Gravity written by John Baez and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-10-24 with Science categories.
This is an introduction to the basic tools of mathematics needed to understand the relation between knot theory and quantum gravity. The book begins with a rapid course on manifolds and differential forms, emphasizing how these provide a proper language for formulating Maxwell's equations on arbitrary spacetimes. The authors then introduce vector bundles, connections and curvature in order to generalize Maxwell theory to the Yang-Mills equations. The relation of gauge theory to the newly discovered knot invariants such as the Jones polynomial is sketched. Riemannian geometry is then introduced in order to describe Einstein's equations of general relativity and show how an attempt to quantize gravity leads to interesting applications of knot theory.
Knots And Applications
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Author : Louis H Kauffman
language : en
Publisher: World Scientific
Release Date : 1995-03-06
Knots And Applications 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 1995-03-06 with categories.
This volume is a collection of research papers devoted to the study of relationships between knot theory and the foundations of mathematics, physics, chemistry, biology and psychology. Included are reprints of the work of Lord Kelvin (Sir William Thomson) on the 19th century theory of vortex atoms, reprints of modern papers on knotted flux in physics and in fluid dynamics and knotted wormholes in general relativity. It also includes papers on Witten's approach to knots via quantum field theory and applications of this approach to quantum gravity and the Ising model in three dimensions. Other papers discuss the topology of RNA folding in relation to invariants of graphs and Vassiliev invariants, the entanglement structures of polymers, the synthesis of molecular Mobius strips and knotted molecules. The book begins with an article on the applications of knot theory to the foundations of mathematics and ends with an article on topology and visual perception. This volume will be of immense interest to all workers interested in new possibilities in the uses of knots and knot theory. Contents:Knot Logic (L H Kauffman)On Vortex AtomsOn Vortex MotionVortex Statics (W Thomson)Connection between Spin, Statistics, and Kinks (D Finkelstein & J Rubinstein)Flux Quantization and Particle Physics (H Jehle)Knot Wormholes in Geometrodynamics? (E W Mielke)Helicity and the Calugareanu Invariant (H K Moffatt & R L Ricca)Witten's Invariant of 3-Dimensional Manifolds: Loop Expansion and Surgery Calculus (L Rozansky)2+1 Dimensional Quantum Gravity as a Gaussian Fermionic System and the 3D-Ising Model (M Martellini & M Rasetti)Vassiliev Knot Invariants and the Structure of RNA Folding (L H Kauffman & Y B Magarshak)The Entanglement Structures of Polymers (A MacArthur)Synthesis and Cutting “In Half” of a Molecular Mobius Strip — Applications of Low Dimensional Topology in Chemistry (D W Walba et al.)Turning a Penrose Triangle Inside Out (T M Cowan) Readership: Mathematicians and mathematical physicists. keywords:Topological Gravity;Quantum Geometrodynanics;Knot Wormholes
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.
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 Science 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 a 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 "Functional Integration and Vassiliev invariants" 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.
Gauge Fields Knots And Gravity
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Author : John C. Baez
language : en
Publisher:
Release Date : 1994
Gauge Fields Knots And Gravity written by John C. Baez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with categories.
Quantum Topology
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Author : Louis H. Kauffman
language : en
Publisher: World Scientific
Release Date : 1993
Quantum Topology 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 1993 with Mathematics categories.
This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum 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 Quantum Gravity
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Author : John C. Baez
language : en
Publisher:
Release Date : 1994
Knots And Quantum Gravity written by John C. Baez and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
Recent work by mathematicians and physicists has uncovered revelatory connections between knot theory and the problem of developing a quantum theory of gravity. This book, the proceedings of a workshop held to bring together researchers in knot theory and quantum gravity, features a number of expository and research papers that will aid significantly in closing the gap between the two disciplines. It will serve as a guide for mathematicians and physicists seeking to understand this rapidly developing area of research. The book represents a state-of-the-art study of current research and progress. The editor is the author of Gauge Fields, Knots, and Gravity (World Scientific), a graduate level text on the topic.