260077 VO Advanced Module Mathematical and Gravitation Physics - Spectral Triples (2009S)
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ab 3.3.2009 Di, Do 16:15-17:45, Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien
Details
Information
Ziele, Inhalte und Methode der Lehrveranstaltung
Spectral Triples consist of an algebra, a Hhilbert space and a Dirac operator. They characterize differential manifolds if the algebra is noncommutative and allow to reconstruct the manifold.
Art der Leistungskontrolle und erlaubte Hilfsmittel
Verbal examen
Mindestanforderungen und Beurteilungsmaßstab
We give the reconstruction proof and discuss noncommutative examples of spectral triples. If one takes a special matrix algebra one obtains the Standard model of particle physics. A well-known class of examples are ispspectral deformations like the noncommutative torus.
Prüfungsstoff
We follow the proof of Alain Connes using noncommutative geometry and functional analysis.
Literatur
Papers by Alain Connes and Varilly, books by Khalkali, by Landi and by Gracia-Bondia, Varilly and Figuero
Zuordnung im Vorlesungsverzeichnis
PD250,320
Letzte Änderung: Fr 31.08.2018 08:55