2006/08/31 by Alain Connes · 7 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies #hep-th
paper · pdf · doi:10.1088/1126-6708/2006/11/081
published as JHEP0611:081,2006 · Typos removed, to appear in JHEP
arxiv created 2006/11/27 · openalex publication_date 2006/11/28 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29
We show that allowing the metric dimension of a space to be independent of its KO-dimension and turning the finite noncommutative geometry F-- whose product with classical 4-dimensional space-time gives the standard model coupled with gravity--into a space of KO-dimension 6 by changing the grading on the antiparticle sector into its opposite, allows to solve three problems of the previous noncommutative geometry interpretation of the standard model of particle physics: The finite geometry F is no longer put in "by hand" but a conceptual understanding of its structure and a classification of its metrics is given. The fermion doubling problem in the fermionic part of the action is resolved. The spectral action of our joint work with Chamseddine now automatically generates the full standard model coupled with gravity with neutrino mixing and see-saw mechanism for neutrino masses. The predictions of the Weinberg angle and the Higgs scattering parameter at unification scale are the same as in our joint work but we also find a mass relation (to be imposed at unification scale).