An Introduction to Noncommutative Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Noncommutative Geometry write by Joseph C. Várilly. This book was released on 2006. An Introduction to Noncommutative Geometry available in PDF, EPUB and Kindle. 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.
An Introduction to Noncommutative Differential Geometry and Its Physical Applications
An Introduction to Noncommutative Differential Geometry and Its Physical Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook An Introduction to Noncommutative Differential Geometry and Its Physical Applications write by J. Madore. This book was released on 1999-06-24. An Introduction to Noncommutative Differential Geometry and Its Physical Applications available in PDF, EPUB and Kindle. A thoroughly revised introduction to non-commutative geometry.
Noncommutative Geometry
Noncommutative Geometry - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Noncommutative Geometry write by Alain Connes. This book was released on 2003-12-15. Noncommutative Geometry available in PDF, EPUB and Kindle. 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 and Particle Physics
Noncommutative Geometry and Particle Physics - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Noncommutative Geometry and Particle Physics write by Walter D. van Suijlekom. This book was released on 2014-07-21. Noncommutative Geometry and Particle Physics available in PDF, EPUB and Kindle. 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.
From Differential Geometry to Non-commutative Geometry and Topology
From Differential Geometry to Non-commutative Geometry and Topology - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook From Differential Geometry to Non-commutative Geometry and Topology write by Neculai S. Teleman. This book was released on 2019-11-10. From Differential Geometry to Non-commutative Geometry and Topology available in PDF, EPUB and Kindle. 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.
