Riemannian and Non-commutative Geometry in Physics

TL;DR

This paper explores the analogy between non-commutative geometry's role in particle physics and Riemannian geometry's role in gravity, aiming to clarify their conceptual relationship.

Contribution

It provides an explanatory perspective on the analogy between non-commutative geometry and Riemannian geometry in the context of physics.

Findings

Non-commutative geometry parallels Riemannian geometry in physical theories.

The paper offers conceptual insights into the geometric foundations of particle physics.

It clarifies the analogy between two geometric frameworks in physics.

Abstract

We feel that non-commutative geometry is to particle physics what Riemannian geometry is to gravity. We try to explain this feeling.