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GR: Gravitation und Relativitätstheorie

GR X: HV X

GR X.1: Hauptvortrag

Freitag, 28. März 2003, 11:45–12:30, A310

Quantum Gravity: A Simple Toy Model — •Hans-Jürgen Matschull¹ and Jorma Louko² — ¹Institut für Physik, Universität Mainz — ²School of Mathematical Sciences, University of Nottingham

The purpose of a toy model, that is, a simplified version of a physical theory is to provide some insight into the main ideas and the principle phenomena explained by the theory, without going into too many technical details.

As a toy model for quantum gravity we have studied the Kepler system, consisting of two pointlike particles interacting with the gravitational field, in a three dimensional spacetime. The model can be quantized consistently using standard techniques. Apart from the basic principles of general relativity and quantum theory, no additional assumptions enter this model.

Some physically interesting effects can be derived, which are usually expected to show up in a full theory of quantum gravity in four spacetime dimensions in a very similar form. For example, one finds a kind of foamy structure of spacetime at small length scales, in the sense that the particles cannot be localized at a point. There is also a quantization of geometry, in the sense that the parameters defining the large scale geometry of spacetime have a discrete spectrum.