Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1993-11-05
Phys.Lett.B324:299-302,1994
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
7 pages, Plain Tex, DFTT 67/93, UCD-93-33
Scientific paper
10.1016/0370-2693(94)90197-X
For spacetimes with the topology $\IR\!\times\!T^2$, the action of (2+1)-dimensional gravity with negative cosmological constant $\La$ is written uniquely in terms of the time-independent traces of holonomies around two intersecting noncontractible paths on $T^2$. The holonomy parameters are related to the moduli on slices of constant mean curvature by a time-dependent canonical transformation which introduces an effective Hamiltonian. The quantisation of the two classically equivalent formulations differs by terms of order $O(\hbar^3)$, negligible for small $|\La|$.
Carlip Steven
Nelson Jerry E.
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