On a Classification of Irreducible Almost-Commutative Geometries IV

Details On a Classification of Irreducible Almost-Commutative Geometries IV On a Classification of Irreducible Almost-Commutative Geometries IV

2006-10-03

arxiv.org/abs/hep-th/0610040v2

J.Math.Phys.49:033502,2008

Physics

High Energy Physics

High Energy Physics - Theory

Revised version for publication in the Journal of Mathematical Physics

Scientific paper

10.1063/1.2863695

In this paper we will classify the finite spectral triples with KO-dimension six, following the classification found in [1,2,3,4], with up to four summands in the matrix algebra. Again, heavy use is made of Kra jewski diagrams [5]. Furthermore we will show that any real finite spectral triple in KO-dimension 6 is automatically S 0 -real. This work has been inspired by the recent paper by Alain Connes [6] and John Barrett [7]. In the classification we find that the standard model of particle physics in its minimal version fits the axioms of noncommutative geometry in the case of KO-dimension six. By minimal version it is meant that at least one neutrino has to be massless and mass-terms mixing particles and antiparticles are prohibited

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