Noncommutative geometry and physics: a review of selected recent results

TL;DR

This paper reviews recent developments in noncommutative geometry's applications to physics, focusing on Moyal deformations of gauge theories and the noncommutative geometry of finite groups like Z_2, with implications for string theory and Kaluza-Klein models.

Contribution

It provides an overview of recent results connecting noncommutative geometry with gauge theories and discrete internal spaces, highlighting new theoretical insights.

Findings

Moyal-type deformations relate to M-theory and open string theories.

Noncommutative geometry of finite groups offers new perspectives on gauge theories.

Explicit example of Z_2 illustrates applications to Kaluza-Klein models.

Abstract

This review is based on two lectures given at the 2000 TMR school in Torino. We discuss two main themes: i) Moyal-type deformations of gauge theories, as emerging from M-theory and open string theories, and ii) the noncommutative geometry of finite groups, with the explicit example of Z_2, and its application to Kaluza-Klein gauge theories on discrete internal spaces.