On a Classification of Irreducible Almost Commutative Geometries

Thomas Schucker (1, 2) , Bruno Iochum (1, 2) , Christophe Stephan (1, 2)

1 CPT - Centre de Physique Théorique - UMR 6207
2 CPT - Centre de Physique Théorique - UMR 7332

We classify all irreducible, almost commutative geometries whose spectral action is dynamically non-degenerate. Heavy use is made of Krajewski's diagrammatic language. The motivation for our definition of dynamical non-degeneracy stems from particle physics where the fermion masses are non-degenerate.

Mots clés: Yang-Mills and other gauge theories

Domaines: Physique des Hautes Energies - Théorie [hep-th]

Thomas Schucker, Bruno Iochum, Christophe Stephan. On a Classification of Irreducible Almost Commutative Geometries. Journal of Mathematical Physics, 2001, 37, pp.100-125. ⟨hal-00002851⟩