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Knots And Feynman Diagrams
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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.
Book Synopsis Invariants of Knots, Graphs, and Feynman Diagrams by :
Download or read book Invariants of Knots, Graphs, and Feynman Diagrams written by and published by . This book was released on 2001 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Invariants of knots, graphs, and Feynman diagrams.
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 2004-02-24 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since discovery of the Jones polynomial, knot theory has enjoyed a virtual explosion of important results and now plays a significant role in modern mathematics. In a unique presentation with contents not found in any other monograph, Knot Theory describes, with full proofs, the main concepts and the latest investigations in the field. The book is divided into six thematic sections. The first part discusses "pre-Vassiliev" knot theory, from knot arithmetics through the Jones polynomial and the famous Kauffman-Murasugi theorem. The second part explores braid theory, including braids in different spaces and simple word recognition algorithms. A section devoted to the Vassiliev knot invariants follows, wherein the author proves that Vassiliev invariants are stronger than all polynomial invariants and introduces Bar-Natan's theory on Lie algebra respresentations and knots. The fourth part describes a new way, proposed by the author, to encode knots by d-diagrams. This method allows the encoding of topological objects by words in a finite alphabet. Part Five delves into virtual knot theory and virtualizations of knot and link invariants. This section includes the author's own important results regarding new invariants of virtual knots. The book concludes with an introduction to knots in 3-manifolds and Legendrian knots and links, including Chekanov's differential graded algebra (DGA) construction. Knot Theory 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 professional reference and will serve equally well as a text for a course on knot theory.
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 528 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.
Book Synopsis Introduction to Feynman Diagrams by : S. M. Bilenky
Download or read book Introduction to Feynman Diagrams written by S. M. Bilenky and published by Elsevier. This book was released on 2013-10-22 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Feynman Diagrams provides Feynman diagram techniques and methods for calculating quantities measured experimentally. The book discusses topics Feynman diagrams intended for experimental physicists. Topics presented include methods for calculating the matrix elements (by perturbation theory) and the basic rules for constructing Feynman diagrams; techniques for calculating cross sections and polarizations; processes in which both leptons and hadrons take part; and the electromagnetic and weak form factors of nucleons. Experimental physicists and graduate students of physics will find value in the book.
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.
Book Synopsis Analytic Properties of Feynman Diagrams in Quantum Field Theory by : I. T. Todorov
Download or read book Analytic Properties of Feynman Diagrams in Quantum Field Theory written by I. T. Todorov and published by Elsevier. This book was released on 2014-05-17 with total page 169 pages. Available in PDF, EPUB and Kindle. Book excerpt: Analytic Properties of Feynman Diagrams in Quantum Field Theory deals with quantum field theory, particularly in the study of the analytic properties of Feynman graphs. This book is an elementary presentation of a self-contained exposition of the majorization method used in the study of these graphs. The author has taken the intermediate position between Eden et al. who assumes the physics of the analytic properties of the S-matrix, containing physical ideas and test results without using the proper mathematical methods, and Hwa and Teplitz, whose works are more mathematically inclined with applications of algebraic topology and homology theory. The book starts with the definition of the quadratic form of a Feynman diagram, and then explains the majorization of Feynman diagrams. The book describes the derivation of spectral representations, the dispersion relations for the nucleon-nucleon scattering amplitude, and for the corresponding partial wave amplitude. The text then analyzes the surface of singularities of a Feynman diagram with notes explaining the Cutkosky rules of the Mandelstam representation for the box diagram. This text is ideal for mathematicians, physicists dealing with quantum theory and mechanics, students, and professors in advanced mathematics.
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.
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.
Book Synopsis Knotted Surfaces and Their Diagrams by : J. Scott Carter
Download or read book Knotted Surfaces and Their Diagrams written by J. Scott Carter and published by American Mathematical Soc.. This book was released on 1998 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this text, the authors develop the theory of knotted surfaces in analogy with the classical case of knotted curves in three-dimensional space. Knotted surface diagrams are defined; the theory of Reidemeister moves is developed; and the braid theory of knotted surfaces is
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.
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 2001 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 a 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 "Functional Integration and Vassiliev invariants" 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.
Book Synopsis Knot Theory and Its Applications by : Kunio Murasugi
Download or read book Knot Theory and Its Applications written by Kunio Murasugi and published by Springer Science & Business Media. This book was released on 2009-12-29 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces the study of knots, providing insights into recent applications in DNA research and graph theory. It sets forth fundamental facts such as knot diagrams, braid representations, Seifert surfaces, tangles, and Alexander polynomials. It also covers more recent developments and special topics, such as chord diagrams and covering spaces. The author avoids advanced mathematical terminology and intricate techniques in algebraic topology and group theory. Numerous diagrams and exercises help readers understand and apply the theory. Each chapter includes a supplement with interesting historical and mathematical comments.
Book Synopsis Virtual Knots: The State Of The Art by : Manturov Vassily Olegovich
Download or read book Virtual Knots: The State Of The Art written by Manturov Vassily Olegovich and published by World Scientific. This book was released on 2012-09-21 with total page 553 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is the first systematic research completely devoted to a comprehensive study of virtual knots and classical knots as its integral part. The book is self-contained and contains up-to-date exposition of the key aspects of virtual (and classical) knot theory.Virtual knots were discovered by Louis Kauffman in 1996. When virtual knot theory arose, it became clear that classical knot theory was a small integral part of a larger theory, and studying properties of virtual knots helped one understand better some aspects of classical knot theory and encouraged the study of further problems. Virtual knot theory finds its applications in classical knot theory. Virtual knot theory occupies an intermediate position between the theory of knots in arbitrary three-manifold and classical knot theory.In this book we present the latest achievements in virtual knot theory including Khovanov homology theory and parity theory due to V O Manturov and graph-link theory due to both authors. By means of parity, one can construct functorial mappings from knots to knots, filtrations on the space of knots, refine many invariants and prove minimality of many series of knot diagrams.Graph-links can be treated as “diagramless knot theory”: such “links” have crossings, but they do not have arcs connecting these crossings. It turns out, however, that to graph-links one can extend many methods of classical and virtual knot theories, in particular, the Khovanov homology and the parity theory.
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 422 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.
Book Synopsis A Guide to Feynman Diagrams in the Many-Body Problem by : Richard D. Mattuck
Download or read book A Guide to Feynman Diagrams in the Many-Body Problem written by Richard D. Mattuck and published by Courier Corporation. This book was released on 2012-08-21 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: Superb introduction for nonspecialists covers Feynman diagrams, quasi particles, Fermi systems at finite temperature, superconductivity, vacuum amplitude, Dyson's equation, ladder approximation, and more. "A great delight." — Physics Today. 1974 edition.
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.
