# Particle Physics from Almost Commutative Spacetimes

April 02, 2012

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.

Keywords:

noncommutative geometry; gauge theory; standard model of particle physics