A model for the motion of a particle in a quantum background
نویسنده
چکیده
We are studying the dynamics of a one-dimensional field in a noncommutative 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 E3 and the Planck length lP 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 E3. 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. ∗[email protected]
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