On a Classification of Irreducible Almost Commutative Geometries

TL;DR

This paper classifies all irreducible, almost commutative geometries with spectral actions that are dynamically non-degenerate, using Krajewski diagrams, motivated by particle physics applications involving fermion mass non-degeneracy.

Contribution

It provides a comprehensive classification of such geometries, advancing the understanding of their structure and relevance in particle physics models.

Findings

Complete classification of irreducible, almost commutative geometries with non-degenerate spectral action

Use of Krajewski diagrams for systematic analysis

Insights into fermion mass structures in geometric models

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.