Embedding variables in finite dimensional models - art. no. 104017

Global problems associated with the transformation from the Arnowitt-Deser- Misner (ADM) to the Kuchar variables are studied. Two models are considered : The Friedmann cosmology with scaler matter and the torus sector of the 2 + 1 gravity. For the Friedmann model, transformations to the Kuchar descrip tion corresponding to three different popular time coordinates are shown to exist on the whole ADM phase space, which becomes a proper subset of the K uchar phase spaces. The 2 + 1 gravity model is shown to admit a description by embedding variables everywhere, even at the points with additional symm etry. The transformation from the Kuchar to the ADM description is, however , a many-to-one transformation there, and so the two descriptions are inequ ivalent for this model, too. The most interesting result is that the new co nstraint surface is free from the conical singularity and the new dynamical equations are linearization stable. However, some residual pathology persi sts in the Kuchar description.