Knots And Feynman Diagrams

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Knots and Feynman Diagrams

Author : Dirk Kreimer
Publisher : Cambridge University Press
ISBN 13 : 9780521587617
Total Pages : 276 pages
Book Rating : 4.5/5 (876 download)

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Book Synopsis Knots and Feynman Diagrams by : Dirk Kreimer

Download or read book Knots and Feynman Diagrams written by Dirk Kreimer and published by Cambridge University Press. This book was released on 2000-07-20 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Introduction to Vassiliev Knot Invariants

Author : S. Chmutov
Publisher : Cambridge University Press
ISBN 13 : 1107020832
Total Pages : 521 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Introduction to Vassiliev Knot Invariants by : S. Chmutov

Download or read book Introduction to Vassiliev Knot Invariants written by S. Chmutov and published by Cambridge University Press. This book was released on 2012-05-24 with total page 521 pages. Available in PDF, EPUB and Kindle. Book excerpt: A detailed exposition of the theory with an emphasis on its combinatorial aspects.

Knots And Physics (Second Edition)

Author : Louis H Kauffman
Publisher : World Scientific
ISBN 13 : 9814502375
Total Pages : 739 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Knots And Physics (Second Edition) by : Louis H Kauffman

Download or read book Knots And Physics (Second Edition) written by Louis H Kauffman and published by World Scientific. This book was released on 1994-01-15 with total page 739 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Diagrammatica

Author : Martinus Veltman
Publisher : Cambridge University Press
ISBN 13 : 113993600X
Total Pages : 302 pages
Book Rating : 4.1/5 (399 download)

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Book Synopsis Diagrammatica by : Martinus Veltman

Download or read book Diagrammatica written by Martinus Veltman and published by Cambridge University Press. This book was released on 1994-06-16 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This author provides an easily accessible introduction to quantum field theory via Feynman rules and calculations in particle physics. His aim is to make clear what the physical foundations of present-day field theory are, to clarify the physical content of Feynman rules. The book begins with a brief review of some aspects of Einstein's theory of relativity that are of particular importance for field theory, before going on to consider the relativistic quantum mechanics of free particles, interacting fields, and particles with spin. The techniques learnt in the chapters are then demonstrated in examples that might be encountered in real accelerator physics. Further chapters contain discussions of renormalization, massive and massless vector fields and unitarity. A final chapter presents concluding arguments concerning quantum electrodynamics. The book includes valuable appendices that review some essential mathematics, including complex spaces, matrices, the CBH equation, traces and dimensional regularization. An appendix containing a comprehensive summary of the rules and conventions used is followed by an appendix specifying the full Lagrangian of the Standard Model and the corresponding Feynman rules. To make the book useful for a wide audience a final appendix provides a discussion of the metric used, and an easy-to-use dictionary connecting equations written with different metrics. Written as a textbook, many diagrams, exercises and examples are included. This book will be used by beginning graduate students taking courses in particle physics or quantum field theory, as well as by researchers as a source and reference book on Feynman diagrams and rules.

Feynman Motives

Author : Matilde Marcolli
Publisher : World Scientific
ISBN 13 : 9814271217
Total Pages : 234 pages
Book Rating : 4.8/5 (142 download)

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Book Synopsis Feynman Motives by : Matilde Marcolli

Download or read book Feynman Motives written by Matilde Marcolli and published by World Scientific. This book was released on 2010 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values in Feynman integrals calculations observed by Broadhurst and Kreimer. Two different approaches to the subject are described. The first, a OC bottom-upOCO approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach, which grew out of work of BlochOCoEsnaultOCoKreimer and was more recently developed in joint work of Paolo Aluffi and the author, leads to algebro-geometric and motivic versions of the Feynman rules of quantum field theory and concentrates on explicit constructions of motives and classes in the Grothendieck ring of varieties associated to Feynman integrals. While the varieties obtained in this way can be arbitrarily complicated as motives, the part of the cohomology that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, OC top-downOCO approach to the problem, developed in the work of Alain Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization of perturbative scalar field theories, obtained in the form of a RiemannOCoHilbert correspondence, with Tannakian categories of mixed Tate motives. The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity theory, Hodge structures, arithmetic geometry, supermanifolds, algebraic and non-commutative geometry. The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Partly based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it can also be used by graduate students interested in working in this area. Sample Chapter(s). Chapter 1: Perturbative quantum field theory and Feynman diagrams (350 KB). Contents: Perturbative Quantum Field Theory and Feynman Diagrams; Motives and Periods; Feynman Integrals and Algebraic Varieties; Feynman Integrals and GelfandOCoLeray Forms; ConnesOCoKreimer Theory in a Nutshell; The RiemannOCoHilbert Correspondence; The Geometry of DimReg; Renormalization, Singularities, and Hodge Structures; Beyond Scalar Theories. Readership: Graduate students and researchers in mathematical physics and theoretical physics.

The Interface of Knots and Physics

Author : Louis H. Kauffman
Publisher : American Mathematical Soc.
ISBN 13 : 0821803808
Total Pages : 221 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Interface of Knots and Physics by : Louis H. Kauffman

Download or read book The Interface of Knots and Physics written by Louis H. Kauffman and published by American Mathematical Soc.. This book was released on 1996 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

An Introduction to Quantum and Vassiliev Knot Invariants

Author : David M. Jackson
Publisher : Springer
ISBN 13 : 3030052133
Total Pages : 425 pages
Book Rating : 4.0/5 (3 download)

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Book Synopsis An Introduction to Quantum and Vassiliev Knot Invariants by : David M. Jackson

Download or read book An Introduction to Quantum and Vassiliev Knot Invariants written by David M. Jackson and published by Springer. This book was released on 2019-05-04 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible introduction to knot theory, focussing on Vassiliev invariants, quantum knot invariants constructed via representations of quantum groups, and how these two apparently distinct theories come together through the Kontsevich invariant. Consisting of four parts, the book opens with an introduction to the fundamentals of knot theory, and to knot invariants such as the Jones polynomial. The second part introduces quantum invariants of knots, working constructively from first principles towards the construction of Reshetikhin-Turaev invariants and a description of how these arise through Drinfeld and Jimbo's quantum groups. Its third part offers an introduction to Vassiliev invariants, providing a careful account of how chord diagrams and Jacobi diagrams arise in the theory, and the role that Lie algebras play. The final part of the book introduces the Konstevich invariant. This is a universal quantum invariant and a universal Vassiliev invariant, and brings together these two seemingly different families of knot invariants. The book provides a detailed account of the construction of the Jones polynomial via the quantum groups attached to sl(2), the Vassiliev weight system arising from sl(2), and how these invariants come together through the Kontsevich invariant.

Knot Theory

Author : Vassily Olegovich Manturov
Publisher : CRC Press
ISBN 13 : 1351359126
Total Pages : 507 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Knot Theory by : Vassily Olegovich Manturov

Download or read book Knot Theory written by Vassily Olegovich Manturov and published by CRC Press. This book was released on 2018-04-17 with total page 507 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 Applications

Author : Thaddeus M Cowan
Publisher : World Scientific
ISBN 13 : 9814501433
Total Pages : 492 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Knots And Applications by : Thaddeus M Cowan

Download or read book Knots And Applications written by Thaddeus M Cowan and published by World Scientific. This book was released on 1995-03-06 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topological Geometrodynamics

Author : Matti Pitkanen
Publisher : Bentham Science Publishers
ISBN 13 : 1681081792
Total Pages : 1235 pages
Book Rating : 4.6/5 (81 download)

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Book Synopsis Topological Geometrodynamics by : Matti Pitkanen

Download or read book Topological Geometrodynamics written by Matti Pitkanen and published by Bentham Science Publishers. This book was released on 2016-03-03 with total page 1235 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 '96: Proceedings Of The Fifth International Research Institute Of Mathematical Society Of Japan

Author : S Suzuki
Publisher : World Scientific
ISBN 13 : 9814546283
Total Pages : 614 pages
Book Rating : 4.8/5 (145 download)

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Book Synopsis Knots '96: Proceedings Of The Fifth International Research Institute Of Mathematical Society Of Japan by : S Suzuki

Download or read book Knots '96: Proceedings Of The Fifth International Research Institute Of Mathematical Society Of Japan written by S Suzuki and published by World Scientific. This book was released on 1997-04-19 with total page 614 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the proceedings of an international conference on knot theory held in July 1996 at Waseda University Conference Center. It was organised by the International Research Institute of Mathematical Society of Japan. The conference was attended by nearly 180 mathematicians from Japan and 14 other countries. Most of them were specialists in knot theory. The volume contains 43 papers, which deal with significant current research in knot theory, low-dimensional topology and related topics.The volume includes papers by the following invited speakers: G Burde, R Fenn, L H Kauffman, J Levine, J M Montesinos(-A), H R Morton, K Murasugi, T Soma, and D W Sumners.

The Mathematics of Knots

Author : Markus Banagl
Publisher : Springer Science & Business Media
ISBN 13 : 3642156371
Total Pages : 363 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis The Mathematics of Knots by : Markus Banagl

Download or read book The Mathematics of Knots written by Markus Banagl and published by Springer Science & Business Media. This book was released on 2010-11-25 with total page 363 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume grew out of the Heidelberg Knot Theory Semester, organized by the editors in winter 2008/09 at Heidelberg University. The contributed papers bring the reader up to date on the currently most actively pursued areas of mathematical knot theory and its applications in mathematical physics and cell biology. Both original research and survey articles are presented; numerous illustrations support the text. The book will be of great interest to researchers in topology, geometry, and mathematical physics, graduate students specializing in knot theory, and cell biologists interested in the topology of DNA strands.

Quantum Invariants

Author : Tomotada Ohtsuki
Publisher : World Scientific
ISBN 13 : 9789812811172
Total Pages : 516 pages
Book Rating : 4.8/5 (111 download)

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Book Synopsis Quantum Invariants by : Tomotada Ohtsuki

Download or read book Quantum Invariants written by Tomotada Ohtsuki and published by World Scientific. This book was released on 2002 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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."

Knots and Physics

Author : Louis H. Kauffman
Publisher : World Scientific
ISBN 13 : 9814383007
Total Pages : 865 pages
Book Rating : 4.8/5 (143 download)

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Book Synopsis Knots and Physics by : Louis H. Kauffman

Download or read book Knots and Physics written by Louis H. Kauffman and published by World Scientific. This book was released on 2013 with total page 865 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

When Form Becomes Substance

Author : Luciano Boi
Publisher : Springer Nature
ISBN 13 : 3030831256
Total Pages : 607 pages
Book Rating : 4.0/5 (38 download)

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Book Synopsis When Form Becomes Substance by : Luciano Boi

Download or read book When Form Becomes Substance written by Luciano Boi and published by Springer Nature. This book was released on 2022-11-30 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This interdisciplinary volume collects contributions from experts in their respective fields with as common theme diagrams. Diagrams play a fundamental role in the mathematical visualization and philosophical analysis of forms in space. Some of the most interesting and profound recent developments in contemporary sciences, whether in topology, geometry, dynamic systems theory, quantum field theory or string theory, have been made possible by the introduction of new types of diagrams, which, in addition to their essential role in the discovery of new classes of spaces and phenomena, have contributed to enriching and clarifying the meaning of the operations, structures and properties that are at the heart of these spaces and phenomena. The volume gives a closer look at the scope and the nature of diagrams as constituents of mathematical and physical thought, their function in contemporary artistic work, and appraise, in particular, the actual importance of the diagrams of knots, of braids, of fields, of interaction, of strings in topology and geometry, in quantum physics and in cosmology, but also in theory of perception, in plastic arts and in philosophy. The editors carefully curated this volume to be an inspiration to students and researchers in philosophy, phenomenology, mathematics and the sciences, as well as artists, musicians and the general interested audience.

50 Years Of The Renormalization Group: Dedicated To The Memory Of Michael E Fisher

Author : Amnon Aharony
Publisher : World Scientific
ISBN 13 : 9811282390
Total Pages : 912 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis 50 Years Of The Renormalization Group: Dedicated To The Memory Of Michael E Fisher by : Amnon Aharony

Download or read book 50 Years Of The Renormalization Group: Dedicated To The Memory Of Michael E Fisher written by Amnon Aharony and published by World Scientific. This book was released on 2024-07-26 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions in the book are devoted to the memory of Michael E Fisher, and hence include many personal memories from people whose work was influenced by him. Also, the book is a collection of articles from leaders in the field of phase transitions and critical phenomena, to celebrate 50 years of the renormalization group and the 1972 paper by Wilson and Fisher. Many of the articles review, in tutorial form, the progress in the fields of phase transitions and the renormalization group.

Knots And Physics (Third Edition)

Author : Louis H Kauffman
Publisher : World Scientific
ISBN 13 : 9814494097
Total Pages : 788 pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Knots And Physics (Third Edition) by : Louis H Kauffman

Download or read book Knots And Physics (Third Edition) written by Louis H Kauffman and published by World Scientific. This book was released on 2001-07-26 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.