1993/11/19 by Kiyoshi Ezawa · 1 citation
Physics and Astronomy · #hep-th
paper · pdf · doi:10.1103/physrevd.49.5211
published as Phys. Rev. D 49, 5211 (1994) · 37pages Latex (6 figures not included)
arxiv created 1993/11/19 · arxiv updated 2013/11/13
Two canonical formulations of the Einstein gravity in 2+1 dimensions, namely, the ADM formalism and the Chern-Simons gravity, are investigated in the case of nonvanishing cosmological constant. General arguments for reducing phase spaces of the two formalisms are given when spatial hypersurface is compact. In particular when the space has the topology of a sphere S2 or a torus T2, the spacetimes constructed from these two formulations can be identified and the classical equivalence between the ADM and the CSG is shown. Moreover in the g=1 case the relations between their phase spaces, and therefore between their quantizations, are given in almost the same form as that in the case when the cosmological constant vanishes. There are, however, some modifications, the most remarkable one of which is that the phase space of the CSG is in 1 to 2 correspondence with the one of the ADM when the cosmological constant is negative.