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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 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 Geometry and Physics 3

2013 Mathematics
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Release : 2013
Genre : Mathematics
Kind : eBook
Book Rating : 01X/5 ( reviews)

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Book Synopsis Noncommutative Geometry and Physics 3 by : Giuseppe Dito

Download or read book Noncommutative Geometry and Physics 3 written by Giuseppe Dito. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Noncommutative Geometry and Physics, 3

2013 Mathematics
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Release : 2013
Genre : Mathematics
Kind : eBook
Book Rating : 001/5 ( reviews)

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Book Synopsis Noncommutative Geometry and Physics, 3 by : Giuseppe Dito

Download or read book Noncommutative Geometry and Physics, 3 written by Giuseppe Dito. This book was released on 2013. Available in PDF, EPUB and Kindle. Book excerpt: Noncommutative differential geometry is a novel approach to geometry, aimed in part at applications in physics. It was founded in the early eighties by the 1982 Fields Medalist Alain Connes on the basis of his fundamental works in operator algebras. It is now a very active branch of mathematics with actual and potential applications to a variety of 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. It is an important topic both for mathematics and physics.

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