Non Commutative Geometry In Mathematics And Physics
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Non Commutative Geometry In Mathematics And Physics
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Author : Giuseppe Dito
language : en
Publisher: American Mathematical Soc.
Release Date : 2008
Non Commutative Geometry In Mathematics And Physics written by Giuseppe Dito 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 Mathematics categories.
This volume represents the proceedings of the conference on Topics in Deformation Quantization and Non-Commutative Structures held in Mexico City in September 2005. It contains survey papers and original contributions by various experts in the fields of deformation quantization and non-commutative derived algebraic geometry in the interface between mathematics and physics. It also contains an article based on the XI Memorial Lectures given by M. Kontsevich, which were delivered as part of the conference. This is an excellent introductory volume for readers interested in learning about quantization as deformation, Hopf algebras, and Hodge structures in the framework of non-commutative algebraic geometry.
Noncommutative Geometry
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Author : Alain Connes
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-12-08
Noncommutative Geometry written by Alain Connes 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 2003-12-08 with Mathematics categories.
Noncommutative Geometry is one of the most deep and vital research subjects of present-day Mathematics. Its development, mainly due to Alain Connes, is providing an increasing number of applications and deeper insights for instance in Foliations, K-Theory, Index Theory, Number Theory but also in Quantum Physics of elementary particles. The purpose of the Summer School in Martina Franca was to offer a fresh invitation to the subject and closely related topics; the contributions in this volume include the four main lectures, cover advanced developments and are delivered by prominent specialists.
Noncommutative Geometry
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Author : Alain Connes
language : en
Publisher: Gulf Professional Publishing
Release Date : 1994-11-22
Noncommutative Geometry written by Alain Connes and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-11-22 with Mathematics categories.
This English version of the path-breaking French book on this subject gives the definitive treatment of the revolutionary approach to measure theory, geometry, and mathematical physics developed by Alain Connes. Profusely illustrated and invitingly written, this book is ideal for anyone who wants to know what noncommutative geometry is, what it can do, or how it can be used in various areas of mathematics, quantization, and elementary particles and fields. First full treatment of the subject and its applications Written by the pioneer of this field Broad applications in mathematics Of interest across most fields Ideal as an introduction and survey Examples treated include: the space of Penrose tilings the space of leaves of a foliation the space of irreducible unitary representations of a discrete group the phase space in quantum mechanics the Brillouin zone in the quantum Hall effect A model of space time
Noncommutative Geometry And Number Theory
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Author : Caterina Consani
language : en
Publisher: Springer Science & Business Media
Release Date : 2007-12-18
Noncommutative Geometry And Number Theory written by Caterina Consani 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 2007-12-18 with Mathematics categories.
In recent years, number theory and arithmetic geometry have been enriched by new techniques from noncommutative geometry, operator algebras, dynamical systems, and K-Theory. This volume collects and presents up-to-date research topics in arithmetic and noncommutative geometry and ideas from physics that point to possible new connections between the fields of number theory, algebraic geometry and noncommutative geometry. The articles collected in this volume present new noncommutative geometry perspectives on classical topics of number theory and arithmetic such as modular forms, class field theory, the theory of reductive p-adic groups, Shimura varieties, the local L-factors of arithmetic varieties. They also show how arithmetic appears naturally in noncommutative geometry and in physics, in the residues of Feynman graphs, in the properties of noncommutative tori, and in the quantum Hall effect.
An Introduction To Noncommutative Geometry
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Author : Joseph C. Várilly
language : en
Publisher: European Mathematical Society
Release Date : 2006
An Introduction To Noncommutative Geometry written by Joseph C. Várilly and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Mathematics categories.
Noncommutative geometry, inspired by quantum physics, describes singular spaces by their noncommutative coordinate algebras and metric structures by Dirac-like operators. Such metric geometries are described mathematically by Connes' theory of spectral triples. These lectures, delivered at an EMS Summer School on noncommutative geometry and its applications, provide an overview of spectral triples based on examples. This introduction is aimed at graduate students of both mathematics and theoretical physics. It deals with Dirac operators on spin manifolds, noncommutative tori, Moyal quantization and tangent groupoids, action functionals, and isospectral deformations. The structural framework is the concept of a noncommutative spin geometry; the conditions on spectral triples which determine this concept are developed in detail. The emphasis throughout is on gaining understanding by computing the details of specific examples. The book provides a middle ground between a comprehensive text and a narrowly focused research monograph. It is intended for self-study, enabling the reader to gain access to the essentials of noncommutative geometry. New features since the original course are an expanded bibliography and a survey of more recent examples and applications of spectral triples.
Noncommutative Geometry And Particle Physics
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Author : Walter D. van Suijlekom
language : en
Publisher: Springer
Release Date : 2014-07-21
Noncommutative Geometry And Particle Physics written by Walter D. van Suijlekom and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-21 with Science categories.
This book provides an introduction to noncommutative geometry and presents a number of its recent applications to particle physics. It is intended for graduate students in mathematics/theoretical physics who are new to the field of noncommutative geometry, as well as for researchers in mathematics/theoretical physics with an interest in the physical applications of noncommutative geometry. In the first part, we introduce the main concepts and techniques by studying finite noncommutative spaces, providing a “light” approach to noncommutative geometry. We then proceed with the general framework by defining and analyzing noncommutative spin manifolds and deriving some main results on them, such as the local index formula. In the second part, we show how noncommutative spin manifolds naturally give rise to gauge theories, applying this principle to specific examples. We subsequently geometrically derive abelian and non-abelian Yang-Mills gauge theories, and eventually the full Standard Model of particle physics, and conclude by explaining how noncommutative geometry might indicate how to proceed beyond the Standard Model.
Noncommutative Geometry And Physics
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Author : Alan L. Carey
language : en
Publisher: European Mathematical Society
Release Date : 2011
Noncommutative Geometry And Physics written by Alan L. Carey and has been published by European Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Geometry, Algebraic categories.
This collection of expository articles grew out of the workshop ``Number Theory and Physics'' held in March 2009 at The Erwin Schrodinger International Institute for Mathematical Physics, Vienna. The common theme of the articles is the influence of ideas from noncommutative geometry (NCG) on subjects ranging from number theory to Lie algebras, index theory, and mathematical physics. Matilde Marcolli's article gives a survey of relevant aspects of NCG in number theory, building on an introduction to motives for beginners by Jorge Plazas and Sujatha Ramdorai. A mildly unconventional view of index theory, from the viewpoint of NCG, is described in the article by Alan Carey, John Phillips, and Adam Rennie. As developed by Alain Connes and Dirk Kreimer, NCG also provides insight into novel algebraic structures underlying many analytic aspects of quantum field theory. Dominique Manchon's article on pre-Lie algebras fits into this developing research area. This interplay of algebraic and analytic techniques also appears in the articles by Christoph Bergbauer, who introduces renormalization theory and Feynman diagram methods, and Sylvie Paycha, who focuses on relations between renormalization and zeta function techniques.
Noncommutative Geometry And Physics 3
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Author : Giuseppe Dito
language : en
Publisher: World Scientific
Release Date : 2013
Noncommutative Geometry And Physics 3 written by Giuseppe Dito and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013 with Mathematics categories.
Noncommutative differential geometry has many actual and potential applications to several domains in physics ranging from solid state to quantization of gravity. The strategy is to formulate usual differential geometry in a somewhat unusual manner, using in particular operator algebras and related concepts, so as to be able to plug in noncommutativity in a natural way. Algebraic tools such as K-theory and cyclic cohomology and homology play an important role in this field.
An Invitation To Noncommutative Geometry
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Author : Masoud Khalkhali
language : en
Publisher: World Scientific
Release Date : 2008
An Invitation To Noncommutative Geometry written by Masoud Khalkhali and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.
A walk in the noncommutative garden / A. Connes and M. Marcolli -- Renormalization of noncommutative quantum field theory / H. Grosse and R. Wulkenhaar -- Lectures on noncommutative geometry / M. Khalkhali -- Noncommutative bundles and instantons in Tehran / G. Landi and W. D. van Suijlekom -- Lecture notes on noncommutative algebraic geometry and noncommutative tori / S. Mahanta -- Lectures on derived and triangulated categories / B. Noohi -- Examples of noncommutative manifolds: complex tori and spherical manifolds / J. Plazas -- D-branes in noncommutative field theory / R. J. Szabo.
Elements Of Noncommutative Geometry
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Author : Jose M. Gracia-Bondia
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Elements Of Noncommutative Geometry written by Jose M. Gracia-Bondia 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 2013-11-27 with Mathematics categories.