02889nam 22004575a 450 991015193750332120091109150325.03-03719-524-X10.4171/024(CKB)3710000000953800(CH-001817-3)41-091109(PPN)17815511X(EXLCZ)99371000000095380020091109j20060630 fy 0engurnn|mmmmamaatxtrdacontentcrdamediacrrdacarrierAn Introduction to Noncommutative Geometry[electronic resource] /Joseph C. VárillyZuerich, Switzerland European Mathematical Society Publishing House20061 online resource (121 pages)EMS Series of Lectures in Mathematics (ELM) ;2523-5176Noncommutative 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 condiditons 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.Differential & Riemannian geometrybicsscRelativistic quantum mechanics & quantum field theorybicsscGlobal analysis, analysis on manifoldsmscFunctional analysismscQuantum theorymscDifferential & Riemannian geometryRelativistic quantum mechanics & quantum field theoryGlobal analysis, analysis on manifoldsFunctional analysisQuantum theory58-xx46-xx81-xxmscVárilly Joseph C.65506ch0018173BOOK9910151937503321Introduction to noncommutative geometry229127UNINA