# The Standard Model in noncommutative geometry: fundamental fermions as internal forms

## TL;DR

This paper classifies all Dirac operators compatible with the Standard Model's finite spectral triple, revealing new insights into the geometric structure underlying fundamental fermions as internal forms.

## Contribution

It provides a complete classification of Dirac operators within the noncommutative geometric framework of the Standard Model, highlighting the role of internal forms.

## Key findings

- All possible Dirac operators classified for the finite spectral triple.
- Identification of conditions for H as a self-Morita equivalence bimodule.
- Enhanced understanding of the geometric structure of fundamental fermions.

## Abstract

Given the algebra, Hilbert space H, grading and real structure of the finite spectral triple of the Standard Model, we classify all possible Dirac operators such that H is a self-Morita equivalence bimodule for the associated Clifford algebra.