Abstract
A (2+1)-dimensional Riemannian space satisfying Einstein's equations is investigated as a model for the quantum theory of gravity. This model does not bear any dynamics as there is only one state in which the system can be found: flat space. However, the kinematical aspects of the model are not trivial. It is shown that Feynman's sum over histories leads to a one-dimensional Hilbert space of state vectors and an explicit representation of the physical state vector is given. Various general properties of the gravitational transition amplitude, in particular the canonical constraints, which were derived for the full fourdimensional theory in a previous paper, are verified with the explicit solution of this model.
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