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These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'*-algebras, module theory and K-theory, spectral calculus, forms and connection theory.Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated.Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content.This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics.
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Contenuti
Noncommutative Spaces and Algebras of Functions.- Projective Systems of Noncommutative Lattices.- Modules as Bundles.- A Few Elements of K-Theory.- The Spectral Calculus.- Noncommutative Differential Forms.- Connections on Modules.- Field Theories on Modules.- Gravity Models.- Quantum Mechanical Models on Noncommutative Lattices.
Le informazioni nella sezione "Su questo libro" possono far riferimento a edizioni diverse di questo titolo.
- EditoreSpringer
- Data di pubblicazione2014
- ISBN 10 3662141094
- ISBN 13 9783662141090
- RilegaturaCopertina flessibile
- LinguaInglese
- Numero di pagine224
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An Introduction to Noncommutative Spaces and Their Geometries
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Condizione: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. This book is a comprehensible introduction for physicists to A. Connes approach to noncommutative geometry.These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative. Codice articolo 5222388
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An Introduction to Noncommutative Spaces and Their Geometries
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Springer Berlin Heidelberg Aug 2014, 2014
ISBN 10: 3662141094
ISBN 13: 9783662141090
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Taschenbuch. Condizione: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'\*-algebras, module theory and K-theory, spectral calculus, forms and connection theory.Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated.Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content.This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics. 224 pp. Englisch. Codice articolo 9783662141090
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An Introduction to Noncommutative Spaces and Their Geometries
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Springer Berlin Heidelberg, 2014
ISBN 10: 3662141094
ISBN 13: 9783662141090
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Taschenbuch. Condizione: Neu. Druck auf Anfrage Neuware - Printed after ordering - These lecture notes are an introduction to several ideas and applications of noncommutative geometry. It starts with a not necessarily commutative but associative algebra which is thought of as the algebra of functions on some 'virtual noncommutative space'. Attention is switched from spaces, which in general do not even exist, to algebras of functions. In these notes, particular emphasis is put on seeing noncommutative spaces as concrete spaces, namely as a collection of points with a topology. The necessary mathematical tools are presented in a systematic and accessible way and include among other things, C'\*-algebras, module theory and K-theory, spectral calculus, forms and connection theory.Application to Yang--Mills, fermionic, and gravity models are described. Also the spectral action and the related invariance under automorphism of the algebra is illustrated.Some recent work on noncommutative lattices is presented. These lattices arose as topologically nontrivial approximations to 'contuinuum' topological spaces. They have been used to construct quantum-mechanical and field-theory models, alternative models to lattice gauge theory, with nontrivial topological content.This book will be essential to physicists and mathematicians with an interest in noncommutative geometry and its uses in physics. Codice articolo 9783662141090
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An Introduction to Noncommutative Spaces and Their Geometries (Lecture Notes in Physics Monographs)
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An Introduction to Noncommutative Spaces and Their Geometries (Lecture Notes in Physics Monographs)
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Paperback. Condizione: Brand New. 1997 edition. 224 pages. 9.30x6.20x0.60 inches. In Stock. Codice articolo x-3662141094
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An Introduction to Noncommutative Spaces and Their Geometries (Lecture Notes in Physics Monographs, 51)
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