Knots And Physics (Second Edition)
Title | Knots And Physics (Second Edition) PDF eBook |
Author | Louis H Kauffman |
Publisher | World Scientific |
Pages | 739 |
Release | 1994-01-15 |
Genre | Mathematics |
ISBN | 9814502375 |
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.
The Geometry and Physics of Knots
Title | The Geometry and Physics of Knots PDF eBook |
Author | Michael Francis Atiyah |
Publisher | Cambridge University Press |
Pages | 112 |
Release | 1990-08-23 |
Genre | Mathematics |
ISBN | 9780521395540 |
These notes deal with an area that lies at the crossroads of mathematics and physics and rest primarily on the pioneering work of Vaughan Jones and Edward Witten, who related polynomial invariants of knots to a topological quantum field theory in 2+1 dimensions.
The Knot Book
Title | The Knot Book PDF eBook |
Author | Colin Conrad Adams |
Publisher | American Mathematical Soc. |
Pages | 330 |
Release | 2004 |
Genre | Mathematics |
ISBN | 0821836781 |
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.
History And Science Of Knots
Title | History And Science Of Knots PDF eBook |
Author | John C Turner |
Publisher | World Scientific |
Pages | 463 |
Release | 1996-05-30 |
Genre | Mathematics |
ISBN | 9814499641 |
This book brings together twenty essays on diverse topics in the history and science of knots. It is divided into five parts, which deal respectively with knots in prehistory and antiquity, non-European traditions, working knots, the developing science of knots, and decorative and other aspects of knots.Its authors include archaeologists who write on knots found in digs of ancient sites (one describes the knots used by the recently discovered Ice Man); practical knotters who have studied the history and uses of knots at sea, for fishing and for various life support activities; a historian of lace; a computer scientist writing on computer classification of doilies; and mathematicians who describe the history of knot theories from the eighteenth century to the present day.In view of the explosion of mathematical theories of knots in the past decade, with consequential new and important scientific applications, this book is timely in setting down a brief, fragmentary history of mankind's oldest and most useful technical and decorative device — the knot.
Knots and Physics
Title | Knots and Physics PDF eBook |
Author | Louis H. Kauffman |
Publisher | World Scientific |
Pages | 865 |
Release | 2013 |
Genre | Mathematics |
ISBN | 9814383007 |
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.
Knots and Applications
Title | Knots and Applications PDF eBook |
Author | Louis H. Kauffman |
Publisher | World Scientific |
Pages | 502 |
Release | 1995 |
Genre | Science |
ISBN | 9789810220044 |
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.
Loops, Knots, Gauge Theories and Quantum Gravity
Title | Loops, Knots, Gauge Theories and Quantum Gravity PDF eBook |
Author | Rodolfo Gambini |
Publisher | Cambridge University Press |
Pages | 344 |
Release | 2000-07-03 |
Genre | Mathematics |
ISBN | 9780521654753 |
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.