Equivalent Quantisations of (2+1)-Dimensional Gravity

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 $O({\hslash }^3)$, negligible for small $|\La|$.

7 pages, Plain Tex, DFTT 67/93, UCD-93-33

References in corpus (3)

• (2+1)-Dimensional Chern-Simons Gravity as a Dirac Square Root
• Invariants of 2+1 Quantum Gravity
• The Modular Group, Operator Ordering, and Time in (2+1)-Dimensional Gravity

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• Quantum Holonomies in (2+1)-Dimensional Gravity
• Quantum geometry from 2+1 AdS quantum gravity on the torus
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• Global constants in (2+1)--dimensional gravity
• Canonical description of Exotic General Massive Gravity
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