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An Introduction to Noncommutative Differential Geometry and Its Physical Applications

1999-06-24 Mathematics
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Release : 1999-06-24
Genre : Mathematics
Kind : eBook
Book Rating : 914/5 ( reviews)

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Book Synopsis An Introduction to Noncommutative Differential Geometry and Its Physical Applications by : J. Madore

Download or read book An Introduction to Noncommutative Differential Geometry and Its Physical Applications written by J. Madore. This book was released on 1999-06-24. Available in PDF, EPUB and Kindle. Book excerpt: A thoroughly revised introduction to non-commutative geometry.

Noncommutative Differential Geometry and Its Applications to Physics

2012-12-06 Science
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Release : 2012-12-06
Genre : Science
Kind : eBook
Book Rating : 047/5 ( reviews)

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Book Synopsis Noncommutative Differential Geometry and Its Applications to Physics by : Yoshiaki Maeda

Download or read book Noncommutative Differential Geometry and Its Applications to Physics written by Yoshiaki Maeda. This book was released on 2012-12-06. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry is a new approach to classical geometry. It was originally used by Fields Medalist A. Connes in the theory of foliations, where it led to striking extensions of Atiyah-Singer index theory. It also may be applicable to hitherto unsolved geometric phenomena and physical experiments. However, noncommutative differential geometry was not well understood even among mathematicians. Therefore, an international symposium on commutative differential geometry and its applications to physics was held in Japan, in July 1999. Topics covered included: deformation problems, Poisson groupoids, operad theory, quantization problems, and D-branes. The meeting was attended by both mathematicians and physicists, which resulted in interesting discussions. This volume contains the refereed proceedings of this symposium. Providing a state of the art overview of research in these topics, this book is suitable as a source book for a seminar in noncommutative geometry and physics.

An Introduction to Noncommutative Geometry

2006 Mathematics
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Release : 2006
Genre : Mathematics
Kind : eBook
Book Rating : 241/5 ( reviews)

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Book Synopsis An Introduction to Noncommutative Geometry by : Joseph C. Várilly

Download or read book An Introduction to Noncommutative Geometry written by Joseph C. Várilly. This book was released on 2006. Available in PDF, EPUB and Kindle. Book excerpt: 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

2003-12-15 Mathematics
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Release : 2003-12-15
Genre : Mathematics
Kind : eBook
Book Rating : 027/5 ( reviews)

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Book Synopsis Noncommutative Geometry by : Alain Connes

Download or read book Noncommutative Geometry written by Alain Connes. This book was released on 2003-12-15. Available in PDF, EPUB and Kindle. Book excerpt: 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

2014-07-21 Science
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Release : 2014-07-21
Genre : Science
Kind : eBook
Book Rating : 627/5 ( reviews)

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Book Synopsis Noncommutative Geometry and Particle Physics by : Walter D. van Suijlekom

Download or read book Noncommutative Geometry and Particle Physics written by Walter D. van Suijlekom. This book was released on 2014-07-21. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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