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 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 are linear, the resulting motion is similar to the standard motion in the classical space . 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