Three-dimensional canonical quantum gravity

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Abstract
General aspects of vielbein representation, ADM formulation and canonical quantization of gravity are discussed using pure gravity in three dimensions as a toy model. The classical part focuses on the role of local observers in general relativity, who will later be identified with quantum observers. A precise definition of gauge symmetries and a classification of inequivalent solutions of Einstein's equations in the dreibein formalism is given as well. In the quantum part the construction of the physical Hilbert space is carried out explicitly for a torus- and cylinder-type space manifold, which has not been done so far. Some conceptual problems of quantum gravity are considered from the point of view of an observer sitting inside the universe.
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