Homogeneous 2+1 Dimensional Gravity in the Ashtekar Formulation
arXiv:gr-qc/9507044 · doi:10.1016/0550-3213(98)00500-8
Abstract
The constraint hypersurfaces defining the Witten and Ashtekar formulations for 2+1 gravity are very different. In particular the constraint hypersurface in the Ashtekar case is not a manifold but consists of several sectors that intersect each other in a complicated way. The issue of how to define a consistent dynamics in such a situation is then rather non-trivial. We discuss this point by working out the details in a simplified (finite dimensional) homogeneous reduction of 2+1 gravity in the Ashtekar formulation.
31 pages, latex