Ashtekar Formulation of 2+1 Gravity on a Torus

Details Ashtekar Formulation of 2+1 Gravity on a Torus Ashtekar Formulation of 2+1 Gravity on a Torus

1992-04-09

arxiv.org/abs/hep-th/9204022v1

Nucl.Phys.B385:571-586,1992

Physics

High Energy Physics

High Energy Physics - Theory

15 pages

Scientific paper

10.1016/0550-3213(92)90059-K

Pure (2+1)-dimensional Einstein gravity is analysed in the Ashtekar formulation, when the spatial manifold is a torus. We have found a set of globally defined observables, forming a closed algebra. This allowed us to solve the quantum constraints, and to show that the reduced phase space of the Ashtekar formulation is greater then the corresponding space of the Witten formulation. Furthermore, we have found a globally defined time variable which satisfies all the requiriments of an extrinsic time variable in quantum gravity.

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