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Quantum Field Theory And Manifold Invariants
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Author :Daniel S. Freed Publisher :American Mathematical Society, IAS/Park City Mathematics Institute ISBN 13 :1470461234 Total Pages :476 pages Book Rating :4.4/5 (74 download)
Book Synopsis Quantum Field Theory and Manifold Invariants by : Daniel S. Freed
Download or read book Quantum Field Theory and Manifold Invariants written by Daniel S. Freed and published by American Mathematical Society, IAS/Park City Mathematics Institute. This book was released on 2021-12-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures from the Graduate Summer School “Quantum Field Theory and Manifold Invariants” held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field. Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.
Book Synopsis Quantum Invariants of Knots and 3-Manifolds by : Vladimir G. Turaev
Download or read book Quantum Invariants of Knots and 3-Manifolds written by Vladimir G. Turaev and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-07-11 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the strong appeal and wide use of this monograph, it is now available in its third revised edition. The monograph gives a systematic treatment of 3-dimensional topological quantum field theories (TQFTs) based on the work of the author with N. Reshetikhin and O. Viro. This subject was inspired by the discovery of the Jones polynomial of knots and the Witten-Chern-Simons field theory. On the algebraic side, the study of 3-dimensional TQFTs has been influenced by the theory of braided categories and the theory of quantum groups.The book is divided into three parts. Part I presents a construction of 3-dimensional TQFTs and 2-dimensional modular functors from so-called modular categories. This gives a vast class of knot invariants and 3-manifold invariants as well as a class of linear representations of the mapping class groups of surfaces. In Part II the technique of 6j-symbols is used to define state sum invariants of 3-manifolds. Their relation to the TQFTs constructed in Part I is established via the theory of shadows. Part III provides constructions of modular categories, based on quantum groups and skein modules of tangles in the 3-space.This fundamental contribution to topological quantum field theory is accessible to graduate students in mathematics and physics with knowledge of basic algebra and topology. It is an indispensable source for everyone who wishes to enter the forefront of this fascinating area at the borderline of mathematics and physics. Contents:Invariants of graphs in Euclidean 3-space and of closed 3-manifoldsFoundations of topological quantum field theoryThree-dimensional topological quantum field theoryTwo-dimensional modular functors6j-symbolsSimplicial state sums on 3-manifoldsShadows of manifolds and state sums on shadowsConstructions of modular categories
Book Synopsis Topological Quantum Field Theory and Four Manifolds by : Jose Labastida
Download or read book Topological Quantum Field Theory and Four Manifolds written by Jose Labastida and published by Springer Science & Business Media. This book was released on 2007-07-18 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emergence of topological quantum ?eld theory has been one of the most important breakthroughs which have occurred in the context of ma- ematical physics in the last century, a century characterizedbyindependent developments of the main ideas in both disciplines, physics and mathematics, which has concluded with two decades of strong interaction between them, where physics, as in previous centuries, has acted as a source of new mat- matics. Topological quantum ?eld theories constitute the core of these p- nomena, although the main drivingforce behind it has been the enormous e?ort made in theoretical particle physics to understand string theory as a theory able to unify the four fundamental interactions observed in nature. These theories set up a new realm where both disciplines pro?t from each other. Although the most striking results have appeared on the mathema- calside,theoreticalphysicshasclearlyalsobene?tted,sincethecorresponding developments have helped better to understand aspects of the fundamentals of ?eld and string theory.
Book Synopsis Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications by : Pavel Mnev
Download or read book Quantum Field Theory: Batalin–Vilkovisky Formalism and Its Applications written by Pavel Mnev and published by American Mathematical Soc.. This book was released on 2019-08-20 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book originated from lecture notes for the course given by the author at the University of Notre Dame in the fall of 2016. The aim of the book is to give an introduction to the perturbative path integral for gauge theories (in particular, topological field theories) in Batalin–Vilkovisky formalism and to some of its applications. The book is oriented toward a graduate mathematical audience and does not require any prior physics background. To elucidate the picture, the exposition is mostly focused on finite-dimensional models for gauge systems and path integrals, while giving comments on what has to be amended in the infinite-dimensional case relevant to local field theory. Motivating examples discussed in the book include Alexandrov–Kontsevich–Schwarz–Zaboronsky sigma models, the perturbative expansion for Chern–Simons invariants of 3-manifolds given in terms of integrals over configurations of points on the manifold, the BF theory on cellular decompositions of manifolds, and Kontsevich's deformation quantization formula.
Author :Daniel S. Freed Publisher :American Mathematical Society, IAS/Park City Mathematics Institute ISBN 13 :1470461234 Total Pages :476 pages Book Rating :4.4/5 (74 download)
Book Synopsis Quantum Field Theory and Manifold Invariants by : Daniel S. Freed
Download or read book Quantum Field Theory and Manifold Invariants written by Daniel S. Freed and published by American Mathematical Society, IAS/Park City Mathematics Institute. This book was released on 2021-12-02 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains lectures from the Graduate Summer School “Quantum Field Theory and Manifold Invariants” held at Park City Mathematics Institute 2019. The lectures span topics in topology, global analysis, and physics, and they range from introductory to cutting edge. Topics treated include mathematical gauge theory (anti-self-dual equations, Seiberg-Witten equations, Higgs bundles), classical and categorified knot invariants (Khovanov homology, Heegaard Floer homology), instanton Floer homology, invertible topological field theory, BPS states and spectral networks. This collection presents a rich blend of geometry and topology, with some theoretical physics thrown in as well, and so provides a snapshot of a vibrant and fast-moving field. Graduate students with basic preparation in topology and geometry can use this volume to learn advanced background material before being brought to the frontiers of current developments. Seasoned researchers will also benefit from the systematic presentation of exciting new advances by leaders in their fields.
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 508 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 Chern-Simons field theory and the Wess-Zumino-Witten model are described as the physical background of the invariants.
Book Synopsis Invariants of Homology 3-Spheres by : Nikolai Saveliev
Download or read book Invariants of Homology 3-Spheres written by Nikolai Saveliev and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book gives a systematic exposition of the diverse ideas and methods in the area, from algebraic topology of manifolds to invariants arising from quantum field theories. The main topics covered include: constructions and classification of homology 3-spheres, Rokhlin invariant, Casson invariant and its extensions, and Floer homology and gauge-theoretical invariants of homology cobordism. Many of the topics covered in the book appear in monograph form for the first time. The book gives a rather broad overview of ideas and methods and provides a comprehensive bibliography. The text will be a valuable source for both the graduate student and researcher in mathematics and theoretical physics.
Book Synopsis Geometric and Topological Methods for Quantum Field Theory by : Hernan Ocampo
Download or read book Geometric and Topological Methods for Quantum Field Theory written by Hernan Ocampo and published by Springer Science & Business Media. This book was released on 2005-06-13 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume offers an introduction, in the form of four extensive lectures, to some recent developments in several active topics at the interface between geometry, topology and quantum field theory. The first lecture is by Christine Lescop on knot invariants and configuration spaces, in which a universal finite-type invariant for knots is constructed as a series of integrals over configuration spaces. This is followed by the contribution of Raimar Wulkenhaar on Euclidean quantum field theory from a statistical point of view. The author also discusses possible renormalization techniques on noncommutative spaces. The third lecture is by Anamaria Font and Stefan Theisen on string compactification with unbroken supersymmetry. The authors show that this requirement leads to internal spaces of special holonomy and describe Calabi-Yau manifolds in detail. The last lecture, by Thierry Fack, is devoted to a K-theory proof of the Atiyah-Singer index theorem and discusses some applications of K-theory to noncommutative geometry. These lectures notes, which are aimed in particular at graduate students in physics and mathematics, start with introductory material before presenting more advanced results. Each chapter is self-contained and can be read independently.
Book Synopsis Quantum Field Theory, Supersymmetry, and Enumerative Geometry by : Daniel S. Freed
Download or read book Quantum Field Theory, Supersymmetry, and Enumerative Geometry written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2006 with total page 297 pages. Available in PDF, EPUB and Kindle. Book excerpt: Each summer the IAS/Park City Mathematics Institute Graduate Summer School gathers some of the best researchers and educators in a particular field to present diverse sets of lectures. This volume presents three weeks of lectures given at the Summer School on Quantum Field Theory, Supersymmetry, and Enumerative Geometry, three very active research areas in mathematics and theoretical physics. With this volume, the Park City Mathematics Institute returns to the general topic of the first institute: the interplay between quantum field theory and mathematics. Two major themes at this institute were supersymmetry and algebraic geometry, particularly enumerative geometry. The volume contains two lecture series on methods of enumerative geometry that have their roots in QFT. The first series covers the Schubert calculus and quantum cohomology. The second discusses methods from algebraic geometry for computing Gromov-Witten invariants. There are also three sets of lectures of a more introductory nature: an overview of classical field theory and supersymmetry, an introduction to supermanifolds, and an introduction to general relativity. This volume is recommended for independent study and is suitable for graduate students and researchers interested in geometry and physics. Information for our distributors: Titles in this series are copublished with the Institute for Advanced Study/Park City Mathematics Institute. Members of the Mathematical Association of America (MAA) and the National Council of Teachers of Mathematics (NCTM) receive a 20% discount from list price.
Book Synopsis Conformal Field Theory and Topology by : Toshitake Kohno
Download or read book Conformal Field Theory and Topology written by Toshitake Kohno and published by American Mathematical Soc.. This book was released on 2002 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis The Link Invariants of the Chern-Simons Field Theory by : E. Guadagnini
Download or read book The Link Invariants of the Chern-Simons Field Theory written by E. Guadagnini and published by Walter de Gruyter. This book was released on 2011-04-20 with total page 329 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do Ceará, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany
Book Synopsis Quantum Field Theory and Topology by : Albert S. Schwarz
Download or read book Quantum Field Theory and Topology written by Albert S. Schwarz and published by Springer Science & Business Media. This book was released on 1993-10-21 with total page 294 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years topology has firmly established itself as an important part of the physicist's mathematical arsenal. It has many applications, first of all in quantum field theory, but increasingly also in other areas of physics. The main focus of this book is on the results of quantum field theory that are obtained by topological methods. Some aspects of the theory of condensed matter are also discussed. Part I is an introduction to quantum field theory: it discusses the basic Lagrangians used in the theory of elementary particles. Part II is devoted to the applications of topology to quantum field theory. Part III covers the necessary mathematical background in summary form. The book is aimed at physicists interested in applications of topology to physics and at mathematicians wishing to familiarize themselves with quantum field theory and the mathematical methods used in this field. It is accessible to graduate students in physics and mathematics.
Book Synopsis Lectures on Field Theory and Topology by : Daniel S. Freed
Download or read book Lectures on Field Theory and Topology written by Daniel S. Freed and published by American Mathematical Soc.. This book was released on 2019-08-23 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: These lectures recount an application of stable homotopy theory to a concrete problem in low energy physics: the classification of special phases of matter. While the joint work of the author and Michael Hopkins is a focal point, a general geometric frame of reference on quantum field theory is emphasized. Early lectures describe the geometric axiom systems introduced by Graeme Segal and Michael Atiyah in the late 1980s, as well as subsequent extensions. This material provides an entry point for mathematicians to delve into quantum field theory. Classification theorems in low dimensions are proved to illustrate the framework. The later lectures turn to more specialized topics in field theory, including the relationship between invertible field theories and stable homotopy theory, extended unitarity, anomalies, and relativistic free fermion systems. The accompanying mathematical explanations touch upon (higher) category theory, duals to the sphere spectrum, equivariant spectra, differential cohomology, and Dirac operators. The outcome of computations made using the Adams spectral sequence is presented and compared to results in the condensed matter literature obtained by very different means. The general perspectives and specific applications fuse into a compelling story at the interface of contemporary mathematics and theoretical physics.
Book Synopsis Advances in Topological Quantum Field Theory by : John M. Bryden
Download or read book Advances in Topological Quantum Field Theory written by John M. Bryden and published by Springer Science & Business Media. This book was released on 2005-03-02 with total page 353 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Quantum Topology by : Louis H. Kauffman
Download or read book Quantum Topology written by Louis H. Kauffman and published by World Scientific. This book was released on 1993 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes a review volume on the relatively new subject of Quantum Topology. Quantum Topology has its inception in the 1984/1985 discoveries of new invariants of knots and links (Jones, Homfly and Kauffman polynomials). These invariants were rapidly connected with quantum groups and methods in statistical mechanics. This was followed by Edward Witten's introduction of methods of quantum field theory into the subject and the formulation by Witten and Michael Atiyah of the concept of topological quantum field theories.This book is a review volume of on-going research activity. The papers derive from talks given at the Special Session on Knot and Topological Quantum Field Theory of the American Mathematical Society held at Dayton, Ohio in the fall of 1992. The book consists of a self-contained article by Kauffman, entitled Introduction to Quantum Topology and eighteen research articles by participants in the special session.This book should provide a useful source of ideas and results for anyone interested in the interface between topology and quantum field theory.
Book Synopsis Quantum Mechanics and Quantum Field Theory by : Jonathan Dimock
Download or read book Quantum Mechanics and Quantum Field Theory written by Jonathan Dimock and published by Cambridge University Press. This book was released on 2011-02-03 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Explaining the concepts of quantum mechanics and quantum field theory in a precise mathematical language, this textbook is an ideal introduction for graduate students in mathematics, helping to prepare them for further studies in quantum physics. The textbook covers topics that are central to quantum physics: non-relativistic quantum mechanics, quantum statistical mechanics, relativistic quantum mechanics and quantum field theory. There is also background material on analysis, classical mechanics, relativity and probability. Each topic is explored through a statement of basic principles followed by simple examples. Around 100 problems throughout the textbook help readers develop their understanding.
Book Synopsis Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners by : Thomas Kerler
Download or read book Non-Semisimple Topological Quantum Field Theories for 3-Manifolds with Corners written by Thomas Kerler and published by Springer. This book was released on 2003-07-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents the (to date) most general approach to combinatorial constructions of topological quantum field theories (TQFTs) in three dimensions. The authors describe extended TQFTs as double functors between two naturally defined double categories: one of topological nature, made of 3-manifolds with corners, the other of algebraic nature, made of linear categories, functors, vector spaces and maps. Atiyah's conventional notion of TQFTs as well as the notion of modular functor from axiomatic conformal field theory are unified in this concept. A large class of such extended modular catergory is constructed, assigning a double functor to every abelian modular category, which does not have to be semisimple.
