Beyond the Standard Model with noncommutative geometry, strolling towards quantum gravity

TL;DR

This paper explores how noncommutative geometry connects various approaches in theoretical physics, including quantum space-time, gauge theories, and models of elementary particles, offering insights into the nature of time and quantum gravity.

Contribution

It provides an overview of noncommutative geometry's diverse applications in quantum gravity, gauge theories, and particle physics, highlighting its original perspective on the nature of time.

Findings

Noncommutative geometry links quantum space-time models with string theory and loop gravity.

It offers a novel viewpoint on the nature of time in quantum gravity.

The paper serves as an introductory overview for a conference session on noncommutative geometry.

Abstract

Noncommutative geometry, in its many incarnations, appears at the crossroad of various researches in theoretical and mathematical physics: from models of quantum space-time (with or without breaking of Lorentz symmetry) to loop gravity and string theory, from early considerations on UV-divergencies in quantum field theory to recent models of gauge theories on noncommutative spacetime, from Connes description of the standard model of elementary particles to recent Pati-Salam like extensions. We list several of these applications, emphasizing also the original point of view brought by noncommutative geometry on the nature of time. This text serves as an introduction to the volume of proceedings of the parallel session "Noncommutative geometry and quantum gravity", as a part of the conference "Conceptual and technical challenges in quantum gravity" organized at the University of Rome "La Sapienza" in September 2014.