# Spectral Noncommutative Geometry, Standard Model and all that

## TL;DR

This paper reviews how spectral noncommutative geometry provides a mathematical framework for the standard model of particle physics, discussing both the theoretical foundations and phenomenological implications, including extensions beyond the standard model.

## Contribution

It offers a comprehensive review of spectral noncommutative geometry applied to the standard model, including detailed discussions of spectral actions and phenomenological aspects.

## Key findings

- Analysis of bosonic and fermionic spectral actions
- Discussion of Euclidean vs. Lorentzian frameworks
- Exploration of extensions beyond the standard model

## Abstract

We review the approach to the standard model of particle interactions based on spectral noncommutative geometry. The paper is (nearly) self-contained and presents both the mathematical and phenomenological aspects. In particular the bosonic spectral action and the fermionic action are discussed in detail, and how they lead to phenomenology. We also discuss the Euclidean vs. Lorentz issues and how to go beyond the standard model in this framework.