A model for the motion of a particle in a quantum background

TL;DR

This paper investigates the motion of a particle in a non-commutative space derived from three-dimensional Euclidean quantum gravity, highlighting differences from classical dynamics as quantum gravity effects.

Contribution

It introduces a model for particle dynamics in a non-commutative quantum background, emphasizing the impact of non-linear effects and proposing a background independent framework.

Findings

Linear dynamics resemble classical motion.

Non-linear dynamics differ due to quantum gravity effects.

Proposes a background independent description.

Abstract

We are studying the dynamics of a one-dimensional field in a non-commutative Euclidean space. The non-commutative space we consider is the one that emerges in the context of three dimensional Euclidean quantum gravity: it is a deformation of the classical Euclidean space and the Planck length plays the role of the deformation parameter. The field is interpreted as a particle which evolves in a quantum background. When the dynamics of the particle is linear, the resulting motion is similar to the standard motion in the classical space. However, non-linear dynamics on the non-commutative space are different from the corresponding non-linear dynamics on the classical space. These discrepencies are interpreted as "quantum gravity" effects. Finally, we propose a background independent description of the propagation of the particle in the quantum geometry.