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Homotopy Quantum Field Theory
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Book Synopsis Homotopy Quantum Field Theory by : Vladimir G. Turaev
Download or read book Homotopy Quantum Field Theory written by Vladimir G. Turaev and published by European Mathematical Society. This book was released on 2010 with total page 300 pages. Available in PDF, EPUB and Kindle. Book excerpt: Homotopy Quantum Field Theory (HQFT) is a branch of Topological Quantum Field Theory founded by E. Witten and M. Atiyah. It applies ideas from theoretical physics to study principal bundles over manifolds and, more generally, homotopy classes of maps from manifolds to a fixed target space. This book is the first systematic exposition of Homotopy Quantum Field Theory. It starts with a formal definition of an HQFT and provides examples of HQFTs in all dimensions. The main body of the text is focused on $2$-dimensional and $3$-dimensional HQFTs. A study of these HQFTs leads to new algebraic objects: crossed Frobenius group-algebras, crossed ribbon group-categories, and Hopf group-coalgebras. These notions and their connections with HQFTs are discussed in detail. The text ends with several appendices including an outline of recent developments and a list of open problems. Three appendices by M. Muger and A. Virelizier summarize their work in this area. The book is addressed to mathematicians, theoretical physicists, and graduate students interested in topological aspects of quantum field theory. The exposition is self-contained and well suited for a one-semester graduate course. Prerequisites include only basics of algebra and topology.
Download or read book Buchdruckerei Passavia written by and published by . This book was released on 1954 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Homotopical Quantum Field Theory by : Donald Yau
Download or read book Homotopical Quantum Field Theory written by Donald Yau and published by World Scientific. This book was released on 2019-11-11 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a general and powerful definition of homotopy algebraic quantum field theory and homotopy prefactorization algebra using a new coend definition of the Boardman-Vogt construction for a colored operad. All of their homotopy coherent structures are explained in details, along with a comparison between the two approaches at the operad level. With chapters on basic category theory, trees, and operads, this book is self-contained and is accessible to graduate students.
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 2013-04-09 with total page 277 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 Quantum Field Theory: Perspective and Prospective by : Cécile Dewitt-Morette
Download or read book Quantum Field Theory: Perspective and Prospective written by Cécile Dewitt-Morette and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: It has been said that `String theorists talk to string theorists and everyone else wonders what they are saying'. This book will be a great help to those researchers who are challenged by modern quantum field theory. Quantum field theory experienced a renaissance in the late 1960s. Here, participants in the Les Houches sessions of 1970/75, now key players in quantum field theory and its many impacts, assess developments in their field of interest and provide guidance to young researchers challenged by these developments, but overwhelmed by their complexities. The book is not a textbook on string theory, rather it is a complement to Polchinski's book on string theory. It is a survey of current problems which have their origin in quantum field theory.
Book Synopsis Differential Topology and Quantum Field Theory by : Charles Nash
Download or read book Differential Topology and Quantum Field Theory written by Charles Nash and published by Elsevier. This book was released on 1991 with total page 404 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
Book Synopsis Mathematical Aspects of Quantum Field Theories by : Damien Calaque
Download or read book Mathematical Aspects of Quantum Field Theories written by Damien Calaque and published by Springer. This book was released on 2015-01-06 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: Despite its long history and stunning experimental successes, the mathematical foundation of perturbative quantum field theory is still a subject of ongoing research. This book aims at presenting some of the most recent advances in the field, and at reflecting the diversity of approaches and tools invented and currently employed. Both leading experts and comparative newcomers to the field present their latest findings, helping readers to gain a better understanding of not only quantum but also classical field theories. Though the book offers a valuable resource for mathematicians and physicists alike, the focus is more on mathematical developments. This volume consists of four parts: The first Part covers local aspects of perturbative quantum field theory, with an emphasis on the axiomatization of the algebra behind the operator product expansion. The second Part highlights Chern-Simons gauge theories, while the third examines (semi-)classical field theories. In closing, Part 4 addresses factorization homology and factorization algebras.
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 Algebraic Structure of String Field Theory by : Martin Doubek
Download or read book Algebraic Structure of String Field Theory written by Martin Doubek and published by Springer Nature. This book was released on 2020-11-22 with total page 223 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a modern presentation of modular operands and their role in string field theory. The authors aim to outline the arguments from the perspective of homotopy algebras and their operadic origin. Part I reviews string field theory from the point of view of homotopy algebras, including A-infinity algebras, loop homotopy (quantum L-infinity) and IBL-infinity algebras governing its structure. Within this framework, the covariant construction of a string field theory naturally emerges as composition of two morphisms of particular odd modular operads. This part is intended primarily for researchers and graduate students who are interested in applications of higher algebraic structures to strings and quantum field theory. Part II contains a comprehensive treatment of the mathematical background on operads and homotopy algebras in a broader context, which should appeal also to mathematicians who are not familiar with string theory.
Book Synopsis Towards the Mathematics of Quantum Field Theory by : Frédéric Paugam
Download or read book Towards the Mathematics of Quantum Field Theory written by Frédéric Paugam and published by Springer Science & Business Media. This book was released on 2014-02-20 with total page 487 pages. Available in PDF, EPUB and Kindle. Book excerpt: This ambitious and original book sets out to introduce to mathematicians (even including graduate students ) the mathematical methods of theoretical and experimental quantum field theory, with an emphasis on coordinate-free presentations of the mathematical objects in use. This in turn promotes the interaction between mathematicians and physicists by supplying a common and flexible language for the good of both communities, though mathematicians are the primary target. This reference work provides a coherent and complete mathematical toolbox for classical and quantum field theory, based on categorical and homotopical methods, representing an original contribution to the literature. The first part of the book introduces the mathematical methods needed to work with the physicists' spaces of fields, including parameterized and functional differential geometry, functorial analysis, and the homotopical geometric theory of non-linear partial differential equations, with applications to general gauge theories. The second part presents a large family of examples of classical field theories, both from experimental and theoretical physics, while the third part provides an introduction to quantum field theory, presents various renormalization methods, and discusses the quantization of factorization algebras.
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 . This book was released on 2019 with total page 202 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.
Author :Igor Olegovich Cherednikov Publisher :Walter de Gruyter GmbH & Co KG ISBN 13 :3110651033 Total Pages :298 pages Book Rating :4.1/5 (16 download)
Book Synopsis Wilson Lines in Quantum Field Theory by : Igor Olegovich Cherednikov
Download or read book Wilson Lines in Quantum Field Theory written by Igor Olegovich Cherednikov and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-12-02 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: The De Gruyter Studies in Mathematical Physics are devoted to the publication of monographs and high-level texts in mathematical physics. They cover topics and methods in fields of current interest, with an emphasis on didactical presentation. The series will enable readers to understand, apply and develop further, with sufficient rigor, mathematical methods to given problems in physics. For this reason, works with a few authors are preferred over edited volumes. The works in this series are aimed at advanced students and researchers in mathematical and theoretical physics. They can also serve as secondary reading for lectures and seminars at advanced levels.
Book Synopsis Anomalies in Quantum Field Theory by : Reinhold A. Bertlmann
Download or read book Anomalies in Quantum Field Theory written by Reinhold A. Bertlmann and published by Oxford University Press. This book was released on 2000-11-02 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the different aspects of the study of anomalies. Much emphasis is now being placed on the formulation of the theory using the mathematical ideas of differential geometry and topology. It includes derivations and calculations
Book Synopsis Uncle Petros and Goldbach's Conjecture by : Apostolos Doxiadis
Download or read book Uncle Petros and Goldbach's Conjecture written by Apostolos Doxiadis and published by Faber & Faber. This book was released on 2012-11-15 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt: Uncle Petros is a family joke. An ageing recluse, he lives alone in a suburb of Athens, playing chess and tending to his garden. If you didn't know better, you'd surely think he was one of life's failures. But his young nephew suspects otherwise. For Uncle Petros, he discovers, was once a celebrated mathematician, brilliant and foolhardy enough to stake everything on solving a problem that had defied all attempts at proof for nearly three centuries - Goldbach's Conjecture. His quest brings him into contact with some of the century's greatest mathematicians, including the Indian prodigy Ramanujan and the young Alan Turing. But his struggle is lonely and single-minded, and by the end it has apparently destroyed his life. Until that is a final encounter with his nephew opens up to Petros, once more, the deep mysterious beauty of mathematics. Uncle Petros and Goldbach's Conjecture is an inspiring novel of intellectual adventure, proud genius, the exhilaration of pure mathematics - and the rivalry and antagonism which torment those who pursue impossible goals.
Book Synopsis Topology for Physicists by : Albert S. Schwarz
Download or read book Topology for Physicists written by Albert S. Schwarz and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 299 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. Topology has profound relevance to quantum field theory-for example, topological nontrivial solutions of the classical equa tions of motion (solitons and instantons) allow the physicist to leave the frame work of perturbation theory. The significance of topology has increased even further with the development of string theory, which uses very sharp topologi cal methods-both in the study of strings, and in the pursuit of the transition to four-dimensional field theories by means of spontaneous compactification. Im portant applications of topology also occur in other areas of physics: the study of defects in condensed media, of singularities in the excitation spectrum of crystals, of the quantum Hall effect, and so on. Nowadays, a working knowledge of the basic concepts of topology is essential to quantum field theorists; there is no doubt that tomorrow this will also be true for specialists in many other areas of theoretical physics. The amount of topological information used in the physics literature is very large. Most common is homotopy theory. But other subjects also play an important role: homology theory, fibration theory (and characteristic classes in particular), and also branches of mathematics that are not directly a part of topology, but which use topological methods in an essential way: for example, the theory of indices of elliptic operators and the theory of complex manifolds.
Book Synopsis Quantum Field Theory Of Point Particles And Strings by : Brian Hatfield
Download or read book Quantum Field Theory Of Point Particles And Strings written by Brian Hatfield and published by CRC Press. This book was released on 2018-03-09 with total page 756 pages. Available in PDF, EPUB and Kindle. Book excerpt: First Published in 2018. Routledge is an imprint of Taylor & Francis, an Informa company.
