ISBN: 9789812384836

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 … Mehr…

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.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 “Knot Theory and Functional Integration” 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.Contents:Physical KnotsStates and the Bracket PolynomialThe Jones Polynomial and Its GeneralizationsBraids and the Jones PolynomialFormal Feynman Diagrams, Bracket as a Vacuum-Vacuum Expectation and the Quantum Group SL(2)qYang-Baxter Models for Specializations of the Homfly PolynomialKnot-Crystals — Classical Knot Theory in a Modern GuiseThe Kauffman PolynomialThree Manifold Invariants from the Jones PolynomialIntegral Heuristics and Witten's InvariantsThe Chromatic PolynomialThe Potts Model and the Dichromatic PolynomialThe Penrose Theory of Spin NetworksKnots and Strings — Knotted StringsDNA and Quantum Field TheoryKnots in Dynamical Systems — The Lorenz Attractorand selected papersReadership: Physicists and mathematicians.Key Features:Provides unique insights into Andrei Sakharov's life, coming from one of Sakharov's closest personal friendsElucidates scientific concepts in simple languageWritten by one of the pioneers of quark theory; ; Scientific, Technical and Medical > Mathematics > Number theory; GBP<

2001, ISBN: 9789812384836

eBooks, eBook Download (PDF), This invaluable book is an introduction to knot and link invariants as generalised amplitudes for a quasi-physical process. The demands of knot theory, coupl… Mehr…

eBooks, eBook Download (PDF), 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.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 âKnot Theory and Functional Integrationâ 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. [PU: World Scientific Publishing Company], Seiten: 788, [ED: 3], World Scientific Publishing Company, 2001<

ISBN: 9789812384836

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 … Mehr…

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.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 "Knot Theory and Functional Integration" 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. World Scientific Topology 9789810241117, 9789810241117 DE,GB,US,ES,IT,FR,MX English Mathematics, World Scientific Publishing Company<

ISBN: 9789812384836

World Scientific Topology 9789810241117,9789810241117 UK,GB,DE,ES,FR,IT,US,CA,MX,AU,NZ 20010726 English Mathematics 3, World Scientific Publishing Company

2001, ISBN: 9789812384836

eBooks, eBook Download (PDF), [PU: World Scientific Publishing Company], [ED: 3], World Scientific Publishing Company, 2001