An Introduction to Noncommutative Spaces and their Geometry

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dc.creatorLandi, Giovanni
dc.date1997-01-16
dc.date.accessioned2026-07-07T09:14:36Z
dc.date.available2026-07-07T09:14:36Z
dc.descriptionThese lectures notes are an intoduction for physicists to several ideas and applications of noncommutative geometry. The necessary mathematical tools are presented in a way which we feel should be accessible to physicists. We illustrate applications to Yang-Mills, fermionic and gravity models, notably we describe the spectral action recently introduced by Chamseddine and Connes. We also present an introduction to recent work on noncommutative lattices. The latter have been used to construct topologically nontrivial quantum mechanical and field theory models, in particular alternative models of lattice gauge theory. Here is the list of sections: 1. Introduction. 2. Noncommutative Spaces and Algebras of Functions. 3. Noncommutative Lattices. 4. Modules as Bundles. 5. The Spectral Calculus. 6. Noncommutative Differential Forms. 7. Connections on Modules. 8. Field Theories on Modules. 9. Gravity Models. 10. Quantum Mechanical Models on Noncommutative Lattices. Appendices: Basic Notions of Topology. The Gel'fand-Naimark-Segal Construction. Hilbert Modules. Strong Morita Equivalence. Partially Ordered Sets. Pseudodifferential Operators
dc.description181 + iv pages, Latex, 26 figures included in the source file. A revised and enlarged version has been published in Lecture Notes in Physics: Monographs, m51 (Springer-Verlag, Berlin Heidelberg, 1997) ISBN 3-540-63509-2
dc.identifierhttps://arxiv.org/abs/hep-th/9701078
dc.identifierhttp://arxiv.org/abs/hep-th/9701078
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/152728
dc.subjectHigh Energy Physics - Theory
dc.subjectQuantum Algebra
dc.titleAn Introduction to Noncommutative Spaces and their Geometry
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