Geometric And Topological Methods For Quantum Field Theory

Author : Hernan Ocampo,Eddy Pariguan,Sylvie Paycha
Publisher : Cambridge University Press
Page : 435 pages
File Size : 44,7 Mb
Release : 2010-04-29
Category : Science
ISBN : 9781139486736

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Geometric and Topological Methods for Quantum Field Theory by Hernan Ocampo,Eddy Pariguan,Sylvie Paycha Pdf

Aimed at graduate students in physics and mathematics, this book provides an introduction to recent developments in several active topics at the interface between algebra, geometry, topology and quantum field theory. The first part of the book begins with an account of important results in geometric topology. It investigates the differential equation aspects of quantum cohomology, before moving on to noncommutative geometry. This is followed by a further exploration of quantum field theory and gauge theory, describing AdS/CFT correspondence, and the functional renormalization group approach to quantum gravity. The second part covers a wide spectrum of topics on the borderline of mathematics and physics, ranging from orbifolds to quantum indistinguishability and involving a manifold of mathematical tools borrowed from geometry, algebra and analysis. Each chapter presents introductory material before moving on to more advanced results. The chapters are self-contained and can be read independently of the rest.

Author : Leonardo Cano,Alexander Cardona,Hern Ocampo,Andr F Reyes Lega
Publisher : World Scientific
Page : 384 pages
File Size : 44,6 Mb
Release : 2016-09-06
Category : Mathematics
ISBN : 9789814730891

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Geometric, Algebraic and Topological Methods for Quantum Field Theory by Leonardo Cano,Alexander Cardona,Hern Ocampo,Andr F Reyes Lega Pdf

Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.

Author : Sylvie Payche
Publisher : World Scientific
Page : 378 pages
File Size : 45,5 Mb
Release : 2014
Category : Science
ISBN : 9789814460057

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Geometric, Algebraic and Topological Methods for Quantum Field Theory by Sylvie Payche Pdf

Based on lectures held at the 7th Villa de Leyva summer school, this book presents an introduction to topics of current interest in the interface of geometry, topology and physics. It is aimed at graduate students in physics or mathematics with interests in geometric, algebraic as well as topological methods and their applications to quantum field theory. This volume contains the written notes corresponding to lectures given by experts in the field. They cover current topics of research in a way that is suitable for graduate students of mathematics or physics interested in the recent developments and interactions between geometry, topology and physics. The book also contains contributions by younger participants, displaying the ample range of topics treated in the school. A key feature of the present volume is the provision of a pedagogical presentation of rather advanced topics, in a way which is suitable for both mathematicians and physicists.

Author : Hernan Ocampo,Sylvie Paycha,Alexander Cardona
Publisher : World Scientific
Page : 495 pages
File Size : 49,9 Mb
Release : 2003
Category : Science
ISBN : 9789812381316

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Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory by Hernan Ocampo,Sylvie Paycha,Alexander Cardona Pdf

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.

Author : Alexander Cardona,Iván Contreras,Andrés F. Reyes-Lega
Publisher : Cambridge University Press
Page : 128 pages
File Size : 54,9 Mb
Release : 2013-05-09
Category : Science
ISBN : 9781107355194

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Geometric and Topological Methods for Quantum Field Theory by Alexander Cardona,Iván Contreras,Andrés F. Reyes-Lega Pdf

Based on lectures given at the renowned Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics.

Author : Luigi Mangiarotti,Gennadi A Sardanashvily,Giovanni Giachetta
Publisher : World Scientific
Page : 715 pages
File Size : 46,7 Mb
Release : 2005-01-27
Category : Science
ISBN : 9789814481144

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Geometric And Algebraic Topological Methods In Quantum Mechanics by Luigi Mangiarotti,Gennadi A Sardanashvily,Giovanni Giachetta Pdf

In the last decade, the development of new ideas in quantum theory, including geometric and deformation quantization, the non-Abelian Berry's geometric factor, super- and BRST symmetries, non-commutativity, has called into play the geometric techniques based on the deep interplay between algebra, differential geometry and topology. The book aims at being a guide to advanced differential geometric and topological methods in quantum mechanics. Their main peculiarity lies in the fact that geometry in quantum theory speaks mainly the algebraic language of rings, modules, sheaves and categories. Geometry is by no means the primary scope of the book, but it underlies many ideas in modern quantum physics and provides the most advanced schemes of quantization.

Author : Alexander Cardona
Publisher : Unknown
Page : 128 pages
File Size : 52,5 Mb
Release : 2013
Category : Geometric quantization
ISBN : 110734557X

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Geometric and Topological Methods for Quantum Field Theory by Alexander Cardona Pdf

"Based on lectures given at the renowed Villa de Leyva summer school, this book provides a unique presentation of modern geometric methods in quantum field theory. Written by experts, it enables readers to enter some of the most fascinating research topics in this subject. Covering a series of topics on geometry, topology, algebra, number theory methods and their applications to quantum field theory, the book covers topics such as Dirac structures, holomorphic bundles and stability, Feynman integrals, geometric aspects of quantum field theory and the standard model, spectral and Riemannian geometry and index theory. This is a valuable guide for graduate students and researchers in physics and mathematics wanting to enter this interesting research field at the borderline between mathematics and physics"--

Author : Alexander Cardona. Iván Contreras. Andrés F. Reyes-Lega
Publisher : Unknown
Page : 128 pages
File Size : 54,6 Mb
Release : 2013
Category : Electronic
ISBN : 1107357691

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Geometric and Topological Methods for Quantum Field Theory by Alexander Cardona. Iván Contreras. Andrés F. Reyes-Lega Pdf

Author : Leonardo Cano
Publisher : Unknown
Page : 385 pages
File Size : 48,8 Mb
Release : 2016
Category : Electronic books
ISBN : 9814730882

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Geometric by Leonardo Cano Pdf

"Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators."--Publisher's website.

Author : Alexander Cardona,Hernan Ocampo,Sylvie Paycha
Publisher : World Scientific
Page : 500 pages
File Size : 48,5 Mb
Release : 2003
Category : Mathematics
ISBN : 9812705066

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Proceedings of the Summer School Geometric and Topological Methods for Quantum Field Theory by Alexander Cardona,Hernan Ocampo,Sylvie Paycha Pdf

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.

Author : Hernan Ocampo,Sylvie Paycha,Andres F Reyes-lega
Publisher : World Scientific
Page : 530 pages
File Size : 54,7 Mb
Release : 2001-04-30
Category : Science
ISBN : 9789814492829

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Geometric Methods For Quantum Field Theory by Hernan Ocampo,Sylvie Paycha,Andres F Reyes-lega Pdf

Both mathematics and mathematical physics have many active areas of research where the interplay between geometry and quantum field theory has proved extremely fruitful. Duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups offer some striking recent examples of modern topics which stand on the borderline between geometry and analysis on the one hand and quantum field theory on the other, where the physicist's and the mathematician's perspective complement each other, leading to new mathematical and physical concepts and results.This volume introduces the reader to some basic mathematical and physical tools and methods required to follow the recent developments in some active areas of mathematical physics, including duality, gauge field theory, geometric quantization, Seiberg-Witten theory, spectral properties and families of Dirac operators, and the geometry of loop groups. It comprises seven self-contained lectures, which should progressively give the reader a precise idea of some of the techniques used in these areas, as well as a few short communications presented by young participants at the school.

Author : Albert S. Schwarz
Publisher : Springer Science & Business Media
Page : 277 pages
File Size : 54,9 Mb
Release : 2013-04-09
Category : Mathematics
ISBN : 9783662029435

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Quantum Field Theory and Topology by Albert S. Schwarz Pdf

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.

Author : Frédéric Paugam
Publisher : Springer Science & Business Media
Page : 485 pages
File Size : 54,5 Mb
Release : 2014-02-20
Category : Science
ISBN : 9783319045641

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Towards the Mathematics of Quantum Field Theory by Frédéric Paugam Pdf

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.

Author : Alexander Cardona,Leonardo Cano,Hernan Ocampo,Andres F. Reyes Lega
Publisher : World Scientific Publishing Company
Page : 372 pages
File Size : 54,7 Mb
Release : 2016-02-28
Category : Mathematics
ISBN : 9814730874

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Proceedings of the Geometric, Algebraic and Topological Methods for Quantum Field Theory 2013 by Alexander Cardona,Leonardo Cano,Hernan Ocampo,Andres F. Reyes Lega Pdf

Based on lectures held at the 8th edition of the series of summer schools in Villa de Leyva since 1999, this book presents an introduction to topics of current interest at the interface of geometry, algebra, analysis, topology and theoretical physics. It is aimed at graduate students and researchers in physics or mathematics, and offers an introduction to the topics discussed in the two weeks of the summer school: operator algebras, conformal field theory, black holes, relativistic fluids, Lie groupoids and Lie algebroids, renormalization methods, spectral geometry and index theory for pseudo-differential operators.

Author : Alexander Cardona,Iván Contreras,Andrés F. Reyes-Lega
Publisher : Cambridge University Press
Page : 395 pages
File Size : 53,5 Mb
Release : 2013-05-09
Category : Mathematics
ISBN : 9781107026834

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Geometric and Topological Methods for Quantum Field Theory by Alexander Cardona,Iván Contreras,Andrés F. Reyes-Lega Pdf

A unique presentation of modern geometric methods in quantum field theory for researchers and graduate students in mathematics and physics.