Coherent States for 3d Deformed Special Relativity: semi-classical points in a quantum flat spacetime

TL;DR

This paper constructs and analyzes coherent states in 3D deformed special relativity to understand quantum spacetime points, exploring their properties and geometric meaning in both Riemannian and Lorentzian cases.

Contribution

It introduces a systematic construction of coherent states for 3D DSR, providing insights into quantum geometry and the notion of spacetime points in deformed relativistic frameworks.

Findings

Coherent states minimize uncertainty relations among spacetime coordinates.

The states have well-defined geometric interpretations.

The analysis applies to both Riemannian and Lorentzian signatures.

Abstract

We analyse the quantum geometry of 3-dimensional deformed special relativity (DSR) and the notion of spacetime points in such a context, identified with coherent states that minimize the uncertainty relations among spacetime coordinates operators. We construct this system of coherent states in both the Riemannian and Lorentzian case, and study their properties and their geometric interpretation.