Freiburg 2008 – scientific programme

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MP: Fachverband Theoretische und Mathematische Grundlagen der Physik

MP 7: Nichtkommutative Geometrie

MP 7.2: Talk

Thursday, March 6, 2008, 14:20–14:40, KGI-HS 1023

Neutrino Masses in Noncommutative Geometry — •Christoph Alexander Stephan — Universität Potsdam, Institut für Mathematik, Am Neuen Palais 10, 14469 Potsdam

During the last two decades Alain Connes developed noncommutative Geometry, which allows to unify two of the basic theories of modern physics: General Relativity and the Standard Model of Particle Physics.

In its original version the noncommutative Standard Model allowed only Dirac-Neutrinos. Recently Alain Connes and John Barrett showed that this is due to the fact that the internal space of noncommutative Geometry is Euclidian in an algebraic sense. If one changes its signature from Euclidian to Minkowskian signature, Majorana mass terms are in principle allowed and the SeeSaw mechanism appears naturally.

In this talk I will give an overview of the different possibilities to introduce neutrino masses in the noncommutative Standard Model à la Connes. Since Majorana masses for right-handed Neutrinos result in an incompatibility with the Connes' axiom of orientability for noncommutative spaces, I will present a model which offers a bypass to the SeeSaw mechanism by enlarging the Standard Model particle content while respecting the whole set of axioms.