Canonical Quantization of (2+1)-Dimensional Gravity

Abstract

We consider the quantum dynamics of both open and closed two- dimensional universes with ``wormholes'' and particles. The wave function is given as a sum of freely propagating amplitudes, emitted from a network of mapping class images of the initial state. Interference between these amplitudes gives non-trivial scattering effects, formally analogous to the optical diffraction by a multidimensional grating; the ``bright lines'' correspond to the most probable geometries.

22 pages, Mexico preprint ICN-UNAM-93-14

References in corpus (6)

• (2+1)-Dimensional Chern-Simons Gravity as a Dirac Square Root
• Quantum Canonical Transformations: Physical Equivalence of Quantum Theories
• A Hamiltonian Formulation of Topological Gravity
• The Modular Group, Operator Ordering, and Time in (2+1)-Dimensional Gravity
• Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus
• Homotopy Invariants and Time Evolution in (2+1)-Dimensional Gravity

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• $2+1$ Covariant Lattice Theory and t'Hooft's Formulation
• Piecewise Flat Gravitational Waves
• 't Hooft's Polygon Approach Hyperbolically Revisited
• Exact Piecewise Flat Gravitational Waves
• Quantum Stability of (2+1)-Spacetimes with Non-Trivial Topology