Canonical quantization of (2+1)-dimensional gravity

1994/01/20 by H. Waelbroeck, Henri Waelbroeck · 2 citations
Mathematics · Physics and Astronomy · #Algorithm #Amplitude #Black Holes and Theoretical Physics #Canonical quantization #Classical mechanics #Cosmology and Gravitation Theories #Diffraction #Mathematics #Noncommutative and Quantum Gravity Theories #Physics #Quantization (signal processing) #Quantum #Quantum gravity #Quantum mechanics #Scattering #Scattering amplitude #Theoretical physics #Wave function #Wormhole #gr-qc

paper · pdf · doi:10.1103/physrevd.50.4982

published as Phys.Rev. D50 (1994) 4982-4992 · 22 pages, Mexico preprint ICN-UNAM-93-14

arxiv created 1994/01/20 · openalex publication_date 1994/10/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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 nontrivial scattering effects, formally analogous to the optical diffraction by a multidimensional grating; ``bright lines'' correspond to the most probable geometries.

Citations

• Quantum canonical transformations. Physical equivalence of quantum theories
• Quantum field theory and the Jones polynomial
• Homotopy invariants and time evolution in (2+1)-dimensional gravity
• 2 + 1 dimensional gravity as an exactly soluble system

Cited by

• (2 + 1) covariant lattice theory and 't Hooft's formulation
• Quantum stability of (2+1)-spacetimes with non-trivial topology: negative curvature cases