Fuzzy worldlines with $\kappa$-Poincar\'e symmetries

TL;DR

This paper introduces a new framework using noncommutative worldlines to analyze quantum-deformed relativistic symmetries, specifically focusing on the $ppa$-Poincare9 model, revealing fuzzy properties of deformed worldlines and events.

Contribution

It develops a novel approach based on noncommutative worldlines for studying $ppa$-Poincare9 symmetries, emphasizing the fuzzy nature of time-like worldlines and events.

Findings

Fuzzy properties of $ppa$-deformed time-like worldlines analyzed.

Reconstruction of spacetime events as crossing points of worldlines.

Identification of fuzziness in the set of reconstructed events.

Abstract

A novel approach to study the properties of models with quantum-deformed relativistic symmetries relies on a noncommutative space of worldlines rather than the usual noncommutative spacetime. In this setting, spacetime can be reconstructed as the set of events, that are identified as the crossing of different worldlines. We lay down the basis for this construction for the $\kappa$-Poincar\'e model, analyzing the fuzzy properties of $\kappa$-deformed time-like worldlines and the resulting fuzziness of the reconstructed events.