On a Classification of Irreducible Almost Commutative Geometries

Abstract

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.

47 pages, 9 figures

References in corpus (9)

• Gravity coupled with matter and foundation of non-commutative geometry
• The Spectral Action Principle
• The Standard Model as a noncommutative geometry: the low energy regime
• Classification of Finite Spectral Triples
• A Farewell To Unimodularity
• Anomaly Cancellation and gauge group of the standard model in NCG
• Spectral action beyond the standard model
• Noncommutative Yang-Mills and Noncommutative Relativity: A Bridge Over Trouble Water
• Constraints on the scalar potential from spectral action principle

Cited by in corpus (31)

• Dark matter with invisible light from heavy double charged leptons of almost-commutative geometry?
• Almost-Commutative Geometries Beyond the Standard Model
• On a Classification of Irreducible Almost-Commutative Geometries IV
• The spectral distance on the Moyal plane
• Particle Physics from Almost Commutative Spacetimes
• New Scalar Fields in Noncommutative Geometry
• Krein spectral triples and the fermionic action
• A survey of spectral models of gravity coupled to matter
• Electrodynamics from Noncommutative Geometry
• On a Classification of Irreducible Almost Commutative Geometries III
• Almost-Commutative Geometries Beyond the Standard Model II: New Colours
• Spectral action and big desert
• Almost-Commutative Geometries Beyond the Standard Model III: Vector Doublets
• Moduli spaces of Dirac operators for finite spectral triples
• A reconstruction theorem for almost-commutative spectral triples
• Intersecting Connes Noncommutative Geometry with Quantum Gravity
• On globally non-trivial almost-commutative manifolds
• Finding the Standard Model of Particle Physics, A Combinatorial Problem
• Seesaw and noncommutative geometry
• Noncommutative circle bundles and new Dirac operators
• On a Classification of Irreducible Almost-Commutative Geometries V
• Going beyond the Standard Model with noncommutative geometry
• A Dark Sector Extension of the Almost-Commutative Standard Model
• The geometry of quantum lens spaces: real spectral triples and bundle structure
• A new algebraic structure in the standard model of particle physics
• Finite temperature corrections and embedded strings in noncommutative geometry and the standard model with neutrino mixing
• Massive Neutrinos in Almost-Commutative Geometry
• Noncommutative geometry, topology and the standard model vacuum
• The Inverse Seesaw Mechanism in Noncommutative Geometry
• Gauge unification in noncommutative geometry
• Krajewski diagrams and the Standard Model