Knots And Feynman Diagrams
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Knots And Feynman Diagrams
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Author : Dirk Kreimer
language : en
Publisher: Cambridge University Press
Release Date : 2000-07-20
Knots And Feynman Diagrams written by Dirk Kreimer 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 2000-07-20 with Mathematics categories.
This volume explains how knot theory and Feynman diagrams can be used to illuminate problems in quantum field theory. The author emphasizes how new discoveries in mathematics have inspired conventional calculational methods for perturbative quantum field theory to become more elegant and potentially more powerful methods. The material illustrates what may possibly be the most productive interface between mathematics and physics. As a result, it will be of interest to graduate students and researchers in theoretical and particle physics as well as mathematics.
Topological Geometrodynamics
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Author : Matti Pitkanen
language : en
Publisher: Bentham Science Publishers
Release Date : 2016-03-03
Topological Geometrodynamics written by Matti Pitkanen and has been published by Bentham Science Publishers this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-03 with Science categories.
Topological geometrodynamics (TGD) is a modification of the theory of general relativity inspired by the problems related to the definition of inertial and gravitational energies in the earlier hypotheses. TGD is also a generalization of super string models. TGD brings forth an elegant theoretical projection of reality and builds upon the work by renowned scientists (Wheeler, Feynman, Penrose, Einstein, Josephson to name a few). In TGD, Physical space-time planes are visualized as four-dimensional surfaces in a certain 8-dimensional space (H). The choice of H is fixed by symmetries of standard model and leads to a geometric mapping of known classical fields and elementary particle numbers. TGD differs from Einstein’s geometrodynamics in the way space-time planes or ‘sheets’ are lumped together. Extending the theory based on fusing number concepts implies a further generalisation of the space-time concept allowing the identification of space-time correlates of cognition and intentionality. Additionally, zero energy ontology forces an extension of quantum measurement theory to a theory of consciousness and a hierarchy of phases is identified. Dark matter is thus predicted with far reaching implications for the understanding of consciousness and living systems. Therefore, it sets a solid foundation for modeling our universe in geometric terms. Topological Geometrodynamics: An Overview explains basic and advanced concepts about TGD. The book covers introductory information and classical TGD concepts before delving into twistor-space theory, particle physics, infinite-dimensional spinor geometry, generalized number theory, Planck constants, and the applications of TGD theory in research. The book is a valuable guide to TDG theory for researchers and advanced graduates in theoretical physics and cosmology.
Knots And Physics Second Edition
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Author : Louis H Kauffman
language : en
Publisher: World Scientific
Release Date : 1994-01-15
Knots And Physics Second Edition 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 1994-01-15 with Mathematics categories.
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.
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.
Knot Theory
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Author : Vassily Olegovich Manturov
language : en
Publisher: CRC Press
Release Date : 2018-04-17
Knot Theory written by Vassily Olegovich Manturov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-04-17 with Mathematics categories.
Over the last fifteen years, the face of knot theory has changed due to various new theories and invariants coming from physics, topology, combinatorics and alge-bra. It suffices to mention the great progress in knot homology theory (Khovanov homology and Ozsvath-Szabo Heegaard-Floer homology), the A-polynomial which give rise to strong invariants of knots and 3-manifolds, in particular, many new unknot detectors. New to this Edition is a discussion of Heegaard-Floer homology theory and A-polynomial of classical links, as well as updates throughout the text. Knot Theory, Second Edition is notable not only for its expert presentation of knot theory’s state of the art but also for its accessibility. It is valuable as a profes-sional reference and will serve equally well as a text for a course on knot theory.
Knots And Physics Third Edition
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Author : Louis H Kauffman
language : en
Publisher: World Scientific
Release Date : 2001-07-26
Knots And Physics Third Edition 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 2001-07-26 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.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.
Complements Of Discriminants Of Smooth Maps
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Author : V. A. Vasilʹev
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Complements Of Discriminants Of Smooth Maps written by V. A. Vasilʹev 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 1994 with Mathematics categories.
* Up-to-date reference on this exciting area of mathematics * Discusses the wide range of applications in topology, algebraic geometry, and catastrophe theory.
New Developments In The Theory Of Knots
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Author : Toshitake Kohno
language : en
Publisher: World Scientific
Release Date : 1990-08-31
New Developments In The Theory Of Knots written by Toshitake Kohno and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990-08-31 with Mathematics categories.
This reprint volume focuses on recent developments in knot theory arising from mathematical physics, especially solvable lattice models, Yang-Baxter equation, quantum group and two dimensional conformal field theory. This volume is helpful to topologists and mathematical physicists because existing articles are scattered in journals of many different domains including Mathematics and Physics. This volume will give an excellent perspective on these new developments in Topology inspired by mathematical physics.
Quantum Invariants
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Author : Tomotada Ohtsuki
language : en
Publisher: World Scientific
Release Date : 2002
Quantum Invariants written by Tomotada Ohtsuki and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Science categories.
This book provides an extensive and self-contained presentation of quantum and related invariants of knots and 3-manifolds. Polynomial invariants of knots, such as the Jones and Alexander polynomials, are constructed as quantum invariants, i.e. invariants derived from representations of quantum groups and from the monodromy of solutions to the Knizhnik-Zamolodchikov equation. With the introduction of the Kontsevich invariant and the theory of Vassiliev invariants, the quantum invariants become well-organized. Quantum and perturbative invariants, the LMO invariant, and finite type invariants of 3-manifolds are discussed. The ChernOCoSimons field theory and the WessOCoZuminoOCoWitten model are described as the physical background of the invariants. Contents: Knots and Polynomial Invariants; Braids and Representations of the Braid Groups; Operator Invariants of Tangles via Sliced Diagrams; Ribbon Hopf Algebras and Invariants of Links; Monodromy Representations of the Braid Groups Derived from the KnizhnikOCoZamolodchikov Equation; The Kontsevich Invariant; Vassiliev Invariants; Quantum Invariants of 3-Manifolds; Perturbative Invariants of Knots and 3-Manifolds; The LMO Invariant; Finite Type Invariants of Integral Homology 3-Spheres. Readership: Researchers, lecturers and graduate students in geometry, topology and mathematical physics."
The Encyclopedia Of Science And Technology
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Author : James Trefil
language : en
Publisher: Routledge
Release Date : 2001-08-24
The Encyclopedia Of Science And Technology written by James Trefil and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-08-24 with History categories.
Edited by acclaimed science writer and physicist James Trefil, the Encyclopedia's 1000 entries combine in-depth coverage with a vivid graphic format to bring every facet of science, technology, and medicine into stunning focus. From absolute zero to the Mesozoic era to semiconductors to the twin paradox, Trefil and his co-authors have an uncanny ability to convey how the universe works and to show readers how to apply that knowledge to everyday problems.