On a classification of irreducible almost-commutative geometries V

2009/01/21 by Jan-Hendrik Jureit, Christoph A. Stephan
Mathematics · Physics and Astronomy · #Advanced Operator Algebra Research #Black Holes and Theoretical Physics #Commutative property #Degenerate energy levels #Fermion #Gauge group #Gauge theory #Higgs boson #Higgs field #Higgs mechanism #Invariant (physics) #Mathematical physics #Mathematics #Noncommutative and Quantum Gravity Theories #Particle physics #Physics #Pure mathematics #Quantum mechanics #Theoretical physics #hep-th

paper · pdf · doi:10.1063/1.3167287

published as J.Math.Phys.50:072301,2009

arxiv created 2009/01/21 · openalex publication_date 2009/07/01 · arxiv updated 2014/11/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We extend a classification of irreducible almost-commutative geometries, whose spectral action is dynamically nondegenerate, to internal algebras that have six simple summands. We find essentially four particle models: an extension of the standard model by a new species of fermions with vectorlike coupling to the gauge group and gauge invariant masses, two versions of the electrostrong model, and a variety of the electrostrong model with Higgs mechanism.

Citations

• Krajewski diagrams and spin lifts
• Composite Dark Matter with Invisible Light from Almost-Commutative Geometry
• Classification of finite spectral triples
• Massive neutrinos in almost-commutative geometry
• Noncommutative geometry and the standard model with neutrino mixing
• On a classification of irreducible almost commutative geometries, a second helping
• On spectral triples in quantum gravity: I
• Dark matter with invisible light from heavy double charged leptons of almost-commutative geometry?
• The Spectral Action Principle
• Finding the standard model of particle physics a combinatorial problem