260077 VO Advanced Module Mathematical and Gravitation Physics - Spectral Triples (2009S)
Labels
ab 3.3.2009 Di, Do 16:15-17:45, Erwin Schrödinger International Institute for Mathematical Physics, Boltzmanngasse 9, 1090 Wien
Details
Information
Aims, contents and method of the course
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.
Assessment and permitted materials
Verbal examen
Minimum requirements and assessment criteria
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.
Examination topics
We follow the proof of Alain Connes using noncommutative geometry and functional analysis.
Reading list
Papers by Alain Connes and Varilly, books by Khalkali, by Landi and by Gracia-Bondia, Varilly and Figuero
Association in the course directory
PD250,320
Last modified: Fr 31.08.2018 08:55