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Equivalent Quantisations of (2+1)-Dimensional Gravity

S. Carlip·J. E. Nelson
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Abstract

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 $|\La|$.

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BibTeXRIS

S. Carlip, J. E. Nelson. 1993-11-05. Equivalent Quantisations of (2+1)-Dimensional Gravity. https://doi.org/10.1016/0370-2693(94)90197-x

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