Knots and Physics (eBook)

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  • 144,922 Words
  • 864 Pages

This invaluable book is an introduction to knot and link invariants as generalized 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.

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 new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.

Contents:
  • Physical Knots
  • States and the Bracket Polynomial
  • The Jones Polynomial and Its Generalizations
  • Braids and the Jones Polynomial
  • Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q
  • Yang–Baxter Models for Specializations of the Homfly Polynomial
  • Knot-Crystals — Classical Knot Theory in a Modern Guise
  • The Kauffman Polynomial
  • Three Manifold Invariants from the Jones Polynomial
  • Integral Heuristics and Witten's Invariants
  • The Chromatic Polynomial
  • The Potts Model and the Dichromatic Polynomial
  • The Penrose Theory of Spin Networks
  • Knots and Strings — Knotted Strings
  • DNA and Quantum Field Theory
  • Knots in Dynamical Systems — The Lorenz Attractor
  • and selected papers

Readership: Physicists and mathematicians.

This invaluable book is an introduction to knot and link invariants as generalized 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.

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 new edition, an article on Virtual Knot Theory and Khovanov Homology has beed added.

Contents:
  • Physical Knots
  • States and the Bracket Polynomial
  • The Jones Polynomial and Its Generalizations
  • Braids and the Jones Polynomial
  • Formal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)q
  • Yang–Baxter Models for Specializations of the Homfly Polynomial
  • Knot-Crystals — Classical Knot Theory in a Modern Guise
  • The Kauffman Polynomial
  • Three Manifold Invariants from the Jones Polynomial
  • Integral Heuristics and Witten's Invariants
  • The Chromatic Polynomial
  • The Potts Model and the Dichromatic Polynomial
  • The Penrose Theory of Spin Networks
  • Knots and Strings — Knotted Strings
  • DNA and Quantum Field Theory
  • Knots in Dynamical Systems — The Lorenz Attractor
  • and selected papers

Readership: Physicists and mathematicians.


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by Louis H Kauffman

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