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

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

2008-07-07

arxiv.org/abs/0807.0969v1

Phys.Rev.D78:105008,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

21 pages

Scientific paper

10.1103/PhysRevD.78.105008

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.

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