EMS series of lectures in mathematics: An Introduction to Noncommutative Geometry - Softcover

Joseph C. Várilly

Softcover

ISBN 10: 3037190248 ISBN 13: 9783037190241

Verlag: EMS Press, 2006

Inhaltsangabe

Noncommutative 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 onexamples. 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.

Details zur Ausgabe

• Verlag: EMS Press
• Erscheinungsdatum: 2006
• Sprache: Englisch
• ISBN 10: 3037190248
• ISBN 13: 9783037190241
• Einband: Taschenbuch
• Auflage: 1
• Anzahl der Seiten: 113
• Kontakt zum Hersteller: Nicht verfügbar
• Verantwortliche Person: Nicht verfügbar