In this paper, we will classify the finite spectral triples with -dimension 6, following the classification found in Iochum, B., Schücker, T., and Stephan, C. A., J. Math. Phys. 45, 5003 (2004); Jureit, J.-H. and Stephan, C. A., J. Math. Phys. 46, 043512 (2005); Schücker, T. (unpublished); Jureit, J.-H., Schücker, T., and Stephan, C. A., J. Math. Phys. 46, 072302 (2005). with up to four summands in the matrix algebra. Again, heavy use is made of Krajewski diagrams [Krajewski, T., J. Geom. Phys. 28, 1 (1998).] This work has been inspired by the recent paper by Connes (unpublished) and Barrett (unpublished). 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 -dimension 6. 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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March 2008
Research Article|
March 07 2008
On a classification of irreducible almost-commutative geometries IV
Jan-Hendrik Jureit;
Jan-Hendrik Jureit
Centre de Physique Théorique,
Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix-Marseille 1 et 2 et Sud Toulon-Var
, Laboratoire Affilié à la FRUMAM (FR 2291), CNRS-Luminy, Case 907, 13288 Marseille Cedex 9, France
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Christoph A. Stephan
Christoph A. Stephan
Centre de Physique Théorique,
Unité Mixte de Recherche (UMR 6207) du CNRS et des Universités Aix-Marseille 1 et 2 et Sud Toulon-Var
, Laboratoire Affilié à la FRUMAM (FR 2291), CNRS-Luminy, Case 907, 13288 Marseille Cedex 9, France
Search for other works by this author on:
a)
Also at Université de Provence and Universität Kiel.
b)
Electronic mail: [email protected].
c)
Electronic mail: [email protected].
J. Math. Phys. 49, 033502 (2008)
Article history
Received:
October 10 2006
Accepted:
January 24 2008
Citation
Jan-Hendrik Jureit, Christoph A. Stephan; On a classification of irreducible almost-commutative geometries IV. J. Math. Phys. 1 March 2008; 49 (3): 033502. https://doi.org/10.1063/1.2863695
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