Model for the motion of a particle in a quantum background

Karim Noui
Phys. Rev. D 78, 105008 – Published 7 November 2008

Abstract

We are studying the dynamics of a one-dimensional field in a noncommutative Euclidean space. The noncommutative 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 E3 and the Planck length P 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 are linear, the resulting motion is similar to the standard motion in the classical space E3. However, nonlinear dynamics on the noncommutative space are different from the corresponding nonlinear dynamics on the classical space. These discrepancies are interpreted as “quantum gravity” effects. Finally, we propose a background independent description of the propagation of the particle in the quantum geometry.

  • Received 1 September 2008

DOI:https://doi.org/10.1103/PhysRevD.78.105008

©2008 American Physical Society

Authors & Affiliations

Karim Noui*

  • Laboratoire de Mathématiques et de PhysiqueThéorique, UMR/CNRS 6083, Fédération Denis Poisson, Faculté des Sciences et Techniques, Parc de Grandmont, 37200 Tours, France

  • *noui@lmpt.univ-tours.fr

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Issue

Vol. 78, Iss. 10 — 15 November 2008

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