Particle Physics from Almost Commutative Spacetimes

TL;DR

This review explores how Connes' noncommutative geometry, especially almost commutative manifolds, can be applied to derive and understand the Standard Model of particle physics and its potential unification with gravity.

Contribution

It introduces noncommutative geometry concepts to physicists and demonstrates their application to the Standard Model and gravity unification.

Findings

Derivation of electrodynamics from noncommutative geometry

Application of noncommutative geometry to the electroweak model

Framework for unifying particle physics with gravity

Abstract

Our aim in this review article is to present the applications of Connes' noncommutative geometry to elementary particle physics. Whereas the existing literature is mostly focused on a mathematical audience, in this article we introduce the ideas and concepts from noncommutative geometry using physicists' terminology, gearing towards the predictions that can be derived from the noncommutative description. Focusing on a light package of noncommutative geometry (so-called 'almost commutative manifolds'), we shall introduce in steps: electrodynamics, the electroweak model, culminating in the full Standard Model. We hope that our approach helps in understanding the role noncommutative geometry could play in describing particle physics models, eventually unifying them with Einstein's (geometrical) theory of gravity.