Bonn 2010 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 10: Noncommutative Geometry

MP 10.2: Talk

Thursday, March 18, 2010, 08:55–09:20, JUR H

Model Building in Noncommutative Geometry — •Christoph Stephan — Institut für Mathematik, Universität Potsdam

Noncommutative geometry (NCG) based on spectral triples allows to unify classical Yang-Mills-Higgs (YMH) theories and General Relativity in a single geometrical framework. The relevant spectral triples contain a finite part which encodes the particle content of the YMH models and is subject to strong geometrical restrictions. These restrictions permit a classification of certain (irreducible) spectral triples and lead to a prominent position of the Standard Model (SM) as a "minimal" finite spectral triple.

I will give a short introduction to the basic ideas of NCG and present a "bottom-up" approach to model building in the framework of NCG. This noncommutative model building kit has led to phenomenologically interesting models beyond the SM. These models extend the fermionic and the gauge sector of the SM as well as the scalar sector.