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What can we learn about quantum gravity from a simple toy model, withoutactually quantizing it? The toy model consists of a finite number of pointparticles, coupled to three dimensional Einstein gravity. It has finitely manyphysical degrees of freedom. These are basically the relative positions of theparticles in spacetime and the conjugate momenta. The resulting reduced phasespace is derived from Einstein gravity as a topological field theory. Thecrucial point is thereby that we do not make any a priori assumptions aboutthis phase space, except that the dynamics of the gravitational field isdefined by the Einstein Hilbert action. This already leads to some interestingfeatures of the reduced phase space, such as a non-commutative structure ofspacetime when the model is quantized.Comment: 72 pages, LeTeX2e, 10 eps figure

The phase space structure of multi-particle models in 2+1 gravity