Quantum Spacetime: a Disambiguation

TL;DR

This paper reviews non-commutative geometry models of quantum spacetime, focusing on the DFR model and its irreducible components, comparing different approaches and their foundational aspects.

Contribution

It provides a comprehensive comparison of various quantum spacetime models, emphasizing the DFR approach and clarifying distinctions among different formulations.

Findings

Clarifies the structure of the DFR model and its irreducible components

Highlights differences in motivations and quantisation methods

Discusses approaches to dynamics and covariance in quantum spacetime

Abstract

We review an approach to non-commutative geometry, where models are constructed by quantisation of the coordinates. In particular we focus on the full DFR model and its irreducible components; the (arbitrary) restriction to a particular irreducible component is often referred to as the "canonical quantum spacetime". The aim is to distinguish and compare the approaches under various points of view, including motivations, prescriptions for quantisation, the choice of mathematical objects and concepts, approaches to dynamics and to covariance.