LEADER 02889nam  22004575a 450 
001 9910151937503321
005 20091109150325.0
010   $a3-03719-524-X
024 70$a10.4171/024
035   $a(CKB)3710000000953800
035   $a(CH-001817-3)41-091109
035   $a(PPN)17815511X
035   $a(EXLCZ)993710000000953800
100   $a20091109j20060630  fy             0
101 0 $aeng
135   $aurnn|mmmmamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
183   $acr$2rdacarrier
200 10$aAn Introduction to Noncommutative Geometry$b[electronic resource] /$fJoseph C. Va?rilly
210 3 $aZuerich, Switzerland $cEuropean Mathematical Society Publishing House$d2006
215   $a1 online resource (121 pages)
225 0 $aEMS Series of Lectures in Mathematics (ELM) ;$x2523-5176
330   $aNoncommutative 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.
606   $aDifferential & Riemannian geometry$2bicssc
606   $aRelativistic quantum mechanics & quantum field theory$2bicssc
606   $aGlobal analysis, analysis on manifolds$2msc
606   $aFunctional analysis$2msc
606   $aQuantum theory$2msc
615 07$aDifferential & Riemannian geometry
615 07$aRelativistic quantum mechanics & quantum field theory
615 07$aGlobal analysis, analysis on manifolds
615 07$aFunctional analysis
615 07$aQuantum theory
686   $a58-xx$a46-xx$a81-xx$2msc
700   $aVa?rilly$b Joseph C.$065506
801  0$bch0018173
906   $aBOOK
912   $a9910151937503321
996   $aIntroduction to noncommutative geometry$9229127
997   $aUNINA