Homogeneous 2+1 Dimensional Gravity in the Ashtekar Formulation

Details Homogeneous 2+1 Dimensional Gravity in the Ashtekar Formulation Homogeneous 2+1 Dimensional Gravity in the Ashtekar Formulation

1995-07-21

arxiv.org/abs/gr-qc/9507044v1

Nucl.Phys.B456:355-376,1995

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

31 pages, latex

Scientific paper

10.1016/0550-3213(98)00500-8

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.

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