A scale-covariant quantum space-time

TL;DR

This paper constructs and analyzes a scale-covariant quantum space-time model with dilation symmetry, revealing loss of locality and triviality of certain field algebras, and discusses prospects for a conformally covariant quantum space-time.

Contribution

It explicitly constructs a noncommutative, scale-covariant quantum space-time model with detailed analysis of its algebraic and physical properties, including symmetry actions.

Findings

Loss of locality in the model

Triviality of certain field algebras

Potential for conformally covariant quantum space-time

Abstract

A noncommutative space-time admitting dilation symmetry was briefly mentioned in the seminal work of Doplicher, Fredenhagen and Roberts. In this paper we explicitly construct the model in details and carry out an in-depth analysis. The C*-algebra that describes this quantum space-time is determined, and it is shown that it admits an action by *-automorphisms of the dilation group, along with the expected Poincar\'e covariance. In order to study the main physical properties of this scale-covariant model, a free scalar neutral field is introduced as a investigation tool. Our key results are then the loss of locality and the irreducibility, or triviality, of special field algebras associated with regions of the ordinary Minkowski space-time. It turns out, in the conclusions, that this analysis allows also to argue on viable ways of constructing a full conformally covariant model for quantum space-time.