Basic Noncommutative Geometry
DOWNLOAD
Download Basic Noncommutative Geometry PDF/ePub or read online books in Mobi eBooks. Click Download or Read Online button to get Basic Noncommutative Geometry book now. This website allows unlimited access to, at the time of writing, more than 1.5 million titles, including hundreds of thousands of titles in various foreign languages. If the content not found or just blank you must refresh this page
Basic Noncommutative Geometry
DOWNLOAD
Author : Masoud Khalkhali
language : en
Publisher: European Mathematical Society
Release Date : 2009
Basic Noncommutative Geometry written by Masoud Khalkhali 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 2009 with Mathematics categories.
"Basic Noncommutative Geometry provides an introduction to noncommutative geometry and some of its applications. The book can be used either as a textbook for a graduate course on the subject or for self-study. It will be useful for graduate students and researchers in mathematics and theoretical physics and all those who are interested in gaining an understanding of the subject. One feature of this book is the wealth of examples and exercises that help the reader to navigate through the subject. While background material is provided in the text and in several appendices, some familiarity with basic notions of functional analysis, algebraic topology, differential geometry and homological algebra at a first year graduate level is helpful. Developed by Alain Connes since the late 1970s, noncommutative geometry has found many applications to long-standing conjectures in topology and geometry and has recently made headways in theoretical physics and number theory. The book starts with a detailed description of some of the most pertinent algebra-geometry correspondences by casting geometric notions in algebraic terms, then proceeds in the second chapter to the idea of a noncommutative space and how it is constructed. The last two chapters deal with homological tools: cyclic cohomology and Connes-Chern characters in K-theory and K-homology, culminating in one commutative diagram expressing the equality of topological and analytic index in a noncommutative setting. Applications to integrality of noncommutative topological invariants are given as well."--Publisher's description.
Noncommutative Geometry
DOWNLOAD
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.
Elements Of Noncommutative Geometry
DOWNLOAD
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.
Noncommutative Geometry And Particle Physics
DOWNLOAD
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.
An Introduction To Noncommutative Geometry
DOWNLOAD
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.
From Differential Geometry To Non Commutative Geometry And Topology
DOWNLOAD
Author : Neculai S. Teleman
language : en
Publisher: Springer Nature
Release Date : 2019-11-10
From Differential Geometry To Non Commutative Geometry And Topology written by Neculai S. Teleman and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-10 with Mathematics categories.
This book aims to provide a friendly introduction to non-commutative geometry. It studies index theory from a classical differential geometry perspective up to the point where classical differential geometry methods become insufficient. It then presents non-commutative geometry as a natural continuation of classical differential geometry. It thereby aims to provide a natural link between classical differential geometry and non-commutative geometry. The book shows that the index formula is a topological statement, and ends with non-commutative topology.
An Introduction To Noncommutative Differential Geometry And Its Physical Applications
DOWNLOAD
Author : J. Madore
language : en
Publisher: Cambridge University Press
Release Date : 1999-06-24
An Introduction To Noncommutative Differential Geometry And Its Physical Applications written by J. Madore 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 1999-06-24 with Mathematics categories.
A thoroughly revised introduction to non-commutative geometry.
Noncommutative Geometry Quantum Fields And Motives
DOWNLOAD
Author : Alain Connes
language : en
Publisher: American Mathematical Soc.
Release Date : 2019-03-13
Noncommutative Geometry Quantum Fields And Motives written by Alain Connes 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 2019-03-13 with Mathematics categories.
The unifying theme of this book is the interplay among noncommutative geometry, physics, and number theory. The two main objects of investigation are spaces where both the noncommutative and the motivic aspects come to play a role: space-time, where the guiding principle is the problem of developing a quantum theory of gravity, and the space of primes, where one can regard the Riemann Hypothesis as a long-standing problem motivating the development of new geometric tools. The book stresses the relevance of noncommutative geometry in dealing with these two spaces. The first part of the book deals with quantum field theory and the geometric structure of renormalization as a Riemann-Hilbert correspondence. It also presents a model of elementary particle physics based on noncommutative geometry. The main result is a complete derivation of the full Standard Model Lagrangian from a very simple mathematical input. Other topics covered in the first part of the book are a noncommutative geometry model of dimensional regularization and its role in anomaly computations, and a brief introduction to motives and their conjectural relation to quantum field theory. The second part of the book gives an interpretation of the Weil explicit formula as a trace formula and a spectral realization of the zeros of the Riemann zeta function. This is based on the noncommutative geometry of the adèle class space, which is also described as the space of commensurability classes of Q-lattices, and is dual to a noncommutative motive (endomotive) whose cyclic homology provides a general setting for spectral realizations of zeros of L-functions. The quantum statistical mechanics of the space of Q-lattices, in one and two dimensions, exhibits spontaneous symmetry breaking. In the low-temperature regime, the equilibrium states of the corresponding systems are related to points of classical moduli spaces and the symmetries to the class field theory of the field of rational numbers and of imaginary quadratic fields, as well as to the automorphisms of the field of modular functions. The book ends with a set of analogies between the noncommutative geometries underlying the mathematical formulation of the Standard Model minimally coupled to gravity and the moduli spaces of Q-lattices used in the study of the zeta function.
Cyclic Homology In Non Commutative Geometry
DOWNLOAD
Author : Joachim Cuntz
language : en
Publisher: Springer
Release Date : 2011-01-23
Cyclic Homology In Non Commutative Geometry written by Joachim Cuntz and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-01-23 with Mathematics categories.
Contributions by three authors treat aspects of noncommutative geometry that are related to cyclic homology. The authors give rather complete accounts of cyclic theory from different points of view. The connections between (bivariant) K-theory and cyclic theory via generalized Chern-characters are discussed in detail. Cyclic theory is the natural setting for a variety of general abstract index theorems. A survey of such index theorems is given and the concepts and ideas involved in these theorems are explained.