Conformal Field Theory And Topology
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Conformal Field Theory And Topology
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Author : Toshitake Kohno
language : en
Publisher: American Mathematical Soc.
Release Date : 2002
Conformal Field Theory And Topology written by Toshitake Kohno 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 2002 with Mathematics categories.
Geometry and physics have been developed with a strong influence on each other. One of the most remarkable interactions between geometry and physics since 1980 has been an application of quantum field theory to topology and differential geometry. This book focuses on a relationship between two-dimensional quantum field theory and three-dimensional topology which has been studied intensively since the discovery of the Jones polynomial in the middle of the 1980s and Witten's invariantfor 3-manifolds derived from Chern-Simons gauge theory. An essential difficulty in quantum field theory comes from infinite-dimensional freedom of a system. Techniques dealing with such infinite-dimensional objects developed in the framework of quantum field theory have been influential in geometryas well. This book gives an accessible treatment for a rigorous construction of topological invariants originally defined as partition functions of fields on manifolds. The book is organized as follows: The Introduction starts from classical mechanics and explains basic background materials in quantum field theory and geometry. Chapter 1 presents conformal field theory based on the geometry of loop groups. Chapter 2 deals with the holonomy of conformal field theory. Chapter 3 treatsChern-Simons perturbation theory. The final chapter discusses topological invariants for 3-manifolds derived from Chern-Simons perturbation theory.
Differential Topology And Quantum Field Theory
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Author : Charles Nash
language : en
Publisher: Elsevier
Release Date : 1991
Differential Topology And Quantum Field Theory written by Charles Nash and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
The remarkable developments in differential topology and how these recent advances have been applied as a primary research tool in quantum field theory are presented here in a style reflecting the genuinely two-sided interaction between mathematical physics and applied mathematics. The author, following his previous work (Nash/Sen: Differential Topology for Physicists, Academic Press, 1983), covers elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory. The explanatory approach serves to illuminate and clarify these theories for graduate students and research workers entering the field for the first time. Treats differential geometry, differential topology, and quantum field theory Includes elliptic differential and pseudo-differential operators, Atiyah-Singer index theory, topological quantum field theory, string theory, and knot theory Tackles problems of quantum field theory using differential topology as a tool
Strings Conformal Fields And Topology
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Author : Michio Kaku
language : en
Publisher:
Release Date : 1991
Strings Conformal Fields And Topology written by Michio Kaku and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mathematics categories.
Topology Geometry And Quantum Field Theory
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Author : Ulrike Luise Tillmann
language : en
Publisher: Cambridge University Press
Release Date : 2004-06-28
Topology Geometry And Quantum Field Theory written by Ulrike Luise Tillmann 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 2004-06-28 with Mathematics categories.
The symposium held in honour of the 60th birthday of Graeme Segal brought together leading physicists and mathematicians. Its topics were centred around string theory, M-theory, and quantum gravity on the one hand, and K-theory, elliptic cohomology, quantum cohomology and string topology on the other. Geometry and quantum physics developed in parallel since the recognition of the central role of non-abelian gauge theory in elementary particle physics in the late seventies and the emerging study of super-symmetry and string theory. With its selection of survey and research articles these proceedings fulfil the dual role of reporting on developments in the field and defining directions for future research. For the first time Graeme Segal's manuscript 'The definition of Conformal Field Theory' is published, which has been greatly influential over more than ten years. An introduction by the author puts it into the present context.
Conformal Field Theory With Gauge Symmetry
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Author : Kenji Ueno
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Conformal Field Theory With Gauge Symmetry written by Kenji Ueno 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 2008 with Conformal invariants categories.
This book presents a systematic approach to conformal field theory with gauge symmetry from the point of view of complex algebraic geometry. After presenting the basic facts of the theory of compact Riemann surfaces and the representation theory of affine Lie algebras in Chapters 1 and 2, conformal blocks for pointed Riemann surfaces with coordinates are constructed in Chapter 3. In Chapter 4 the sheaf of conformal blocks associated to a family of pointed Riemann surfaces withcoordinates is constructed, and in Chapter 5 it is shown that this sheaf supports a projective flat connection-one of the most important facts of conformal field theory. Chapter 6 is devoted to the study of the detailed structure of the conformal field theory over $\mathbb{P}1$.Recently it was shown that modular functors can be constructed from conformal field theory, giving an interesting relationship between algebraic geometry and topological quantum field theory. This book provides a timely introduction to an intensively studied topic of conformal field theory with gauge symmetry by a leading algebraic geometer, and includes all the necessary techniques and results that are used to construct the modular functor.
Topology Geometry And Field Theory Proceedings Of The 31st International Taniguchi Symposium And Proceedings Of The Conference
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Author : Kenji Fukaya
language : en
Publisher: World Scientific
Release Date : 1994-08-31
Topology Geometry And Field Theory Proceedings Of The 31st International Taniguchi Symposium And Proceedings Of The Conference written by Kenji Fukaya and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-08-31 with categories.
Nobel Symposium 129 on Neutrino Physics was held at Haga Slott in Enköping, Sweden during August 19-24, 2004. Invited to the symposium were around 40 globally leading researchers in the field of neutrino physics, both experimental and theoretical.The dominant theme of the lectures was neutrino oscillations, which after several years were recently verified by results from the Super-Kamiokande detector in Kamioka, Japan and the SNO detector in Sudbury, Canada. Discussion focused especially on effects of neutrino oscillations derived from the presence of matter and the fact that three different neutrinos exist. Since neutrino oscillations imply that neutrinos have mass, this is the first experimental observation that fundamentally deviates from the standard model of particle physics. This is a challenge to both theoretical and experimental physics. The various oscillation parameters will be determined with increased precision in new, specially designed experiments. Theoretical physics is working intensively to insert the knowledge that neutrinos have mass into the theoretical models that describe particle physics. The lectures provided a very good description of the intensive situation in the field right now. The topics discussed also included mass models for neutrinos, neutrinos in extra dimensions as well as the “seesaw mechanism,” which provides a good description of why neutrino masses are so small.This book is A4 size and in full color.
Low Dimensional Topology And Quantum Field Theory
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Author : Hugh Osborn
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Low Dimensional Topology And Quantum Field Theory written by Hugh Osborn and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-11 with Science categories.
The motivations, goals and general culture of theoretical physics and mathematics are different. Most practitioners of either discipline have no necessity for most of the time to keep abreast of the latest developments in the other. However on occasion newly developed mathematical concepts become relevant in theoretical physics and the less rigorous theoretical physics framework may prove valuable in understanding and suggesting new theorems and approaches in pure mathematics. Such interdis ciplinary successes invariably cause much rejoicing, as over a prodigal son returned. In recent years the framework provided by quantum field theory and functional in tegrals, developed over half a century in theoretical physics, have proved a fertile soil for developments in low dimensional topology and especially knot theory. Given this background it was particularly pleasing that NATO was able to generously sup port an Advanced Research Workshop to be held in Cambridge, England from 6th to 12th September 1992 with the title Low Dimensional Topology and Quantum Field Theory. Although independently organised this overlapped as far as some speak ers were concerned with a longer term programme with the same title organised by Professor M Green, Professor E Corrigan and Dr R Lickorish. The contents of this proceedings of the workshop demonstrate the breadth of topics now of interest on the interface between theoretical physics and mathematics as well as the sophistication of the mathematical tools required in current theoretical physics.
Topology And Field Theories
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Author : Stephan Stolz
language : en
Publisher: American Mathematical Soc.
Release Date : 2014-04-17
Topology And Field Theories written by Stephan Stolz 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 2014-04-17 with Mathematics categories.
This book is a collection of expository articles based on four lecture series presented during the 2012 Notre Dame Summer School in Topology and Field Theories. The four topics covered in this volume are: Construction of a local conformal field theory associated to a compact Lie group, a level and a Frobenius object in the corresponding fusion category; Field theory interpretation of certain polynomial invariants associated to knots and links; Homotopy theoretic construction of far-reaching generalizations of the topological field theories that Dijkgraf and Witten associated to finite groups; and a discussion of the action of the orthogonal group on the full subcategory of an -category consisting of the fully dualizable objects. The expository style of the articles enables non-experts to understand the basic ideas of this wide range of important topics.
Mathematical Aspects Of Conformal And Topological Field Theories And Quantum Groups
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Author : Paul J. Sally (Jr.)
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Mathematical Aspects Of Conformal And Topological Field Theories And Quantum Groups written by Paul J. Sally (Jr.) 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.
This book contains papers presented by speakers at the AMS-IMS-SIAM Joint Summer Research Conference on Conformal Field Theory, Topological Field Theory and Quantum Groups, held at Mount Holyoke College in June 1992. One group of papers deals with one aspect of conformal field theory, namely, vertex operator algebras or superalgebras and their representations. Another group deals with various aspects of quantum groups. Other topics covered include the theory of knots in three-manifolds, symplectic geometry, and tensor products. This book provides an excellent view of some of the latest developments in this growing field of research.
Geometric And Topological Methods For Quantum Field Theory
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Author : Alexander Cardona
language : en
Publisher: World Scientific
Release Date : 2003-03-21
Geometric And Topological Methods For Quantum Field Theory written by Alexander Cardona and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-03-21 with Mathematics categories.
This volume offers an introduction to recent developments in several active topics of research at the interface between geometry, topology and quantum field theory. These include Hopf algebras underlying renormalization schemes in quantum field theory, noncommutative geometry with applications to index theory on one hand and the study of aperiodic solids on the other, geometry and topology of low dimensional manifolds with applications to topological field theory, Chern-Simons supergravity and the anti de Sitter/conformal field theory correspondence. It comprises seven lectures organized around three main topics, noncommutative geometry, topological field theory, followed by supergravity and string theory, complemented by some short communications by young participants of the school. Contents:Noncommutative Geometry:Hopf Algebras in Noncommutative Geometry (J C Várilly)The Noncommutative Geometry of Aperiodic Solids (J Bellissard)Noncommutative Geometry and Abstract Integration Theory (M-T Benameur)Topological Field Theory:Introduction to Quantum Invariants of 3-Manifolds, Topological Quantum Field Theories and Modular Categories (C Blanchet)An Introduction to Donaldson–Witten Theory (M Mariño)Supergravity and String Theory:(Super)-Gravities Beyond 4 Dimensions (J Zanelli)Introductory Lectures on String Theory and the AdS/CFT Correspondence (A Pankiewicz & S Theisen)Short Communications:Group Contractions and Its Consequences Upon Representations of Different Spatial Symmetry Groups (M Ayala-Sánchez & R W Haase)Phase Anomalies as Trace Anomalies in Chern–Simons Theory (A Cardona)Deligne Cohomology for Orbifolds, Discrete Torsion and B-Fields (E Lupercio & B Uribe) Readership: Graduate students and researchers in theoretical and mathematical physics, as well as geometry and topology. Keywords: