Krajewski diagrams and the Standard Model
arXiv:0809.5137 · doi:10.1063/1.3112622
Abstract
This paper provides a complete list of Krajewski diagrams representing the standard model of particle physics. We will give the possible representations of the algebra and the anomaly free lifts which provide the representation of the standard model gauge group on the fermionic Hilbert space. The algebra representations following from the Krajewski diagrams are not complete in the sense that the corresponding spectral triples do not necessarily obey to the axiom of Poincare duality. This defect may be repaired by adding new particles to the model, i.e. by building models beyond the standard model. The aim of this list of finite spectral triples (up to Poincare duality) is therefore to provide a basis for model building beyond the standard model.
References in corpus (17)
- Gravity coupled with matter and foundation of non-commutative geometry
- Gravity and the standard model with neutrino mixing
- A Lorentzian version of the non-commutative geometry of the standard model of particle physics
- Noncommutative Geometry and the standard model with neutrino mixing
- Dark matter with invisible light from heavy double charged leptons of almost-commutative geometry?
- Classification of Finite Spectral Triples
- Almost-Commutative Geometries Beyond the Standard Model
- On a Classification of Irreducible Almost-Commutative Geometries IV
- On a Classification of Irreducible Almost Commutative Geometries
- A Farewell To Unimodularity
- On a Classification of Irreducible Almost Commutative Geometries, A Second Helping
- Almost-Commutative Geometries Beyond the Standard Model II: New Colours
- Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
- Finding the Standard Model of Particle Physics, A Combinatorial Problem
- Non-commutative geometry and the standard model vacuum
- Finite temperature corrections and embedded strings in noncommutative geometry and the standard model with neutrino mixing
- Massive Neutrinos in Almost-Commutative Geometry