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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 11: Nichtkommutative Geometrie

MP 11.3: Talk

Thursday, March 12, 2009, 14:40–15:00, M010

Noncommutative geometry and its application to the standard model — •Pierre Martinetti — Georg-August Universität, Göttingen

We shall give an overview of the description of the standard model of particle physics minimally coupled to gravity within the framework of noncommutative geometry. Especially we shall study in detail the metric structure of spacetime that emerges from the spectral triple recently proposed by Chamseddine, Connes and Marcolli.

Within this framework points of spacetime acquire an internal structure inherited from the gauge group of the standard model. A distance is defined on this generalized spacetime which is fully encoded by the Yang-Mills gauge fields together with the Higgs field.

We will focus on some explicit examples, underlying the link between this distance and other distances well known by physicst and mathematicians, such has the Carnot-Carathéodory horizontal distance or the Monge-Kantorovitch transport distance.