Comparative Quantizations of (2+1)-Dimensional Gravity

Abstract

We compare three approaches to the quantization of (2+1)-dimensional gravity with a negative cosmological constant: reduced phase space quantization with the York time slicing, quantization of the algebra of holonomies, and quantization of the space of classical solutions. The relationships among these quantum theories allow us to define and interpret time-dependent operators in the ``frozen time'' holonomy formulation.

24 pages, LaTeX, no figures

References in corpus (13)

• (2+1)-Dimensional Chern-Simons Gravity as a Dirac Square Root
• Invariants of 2+1 Quantum Gravity
• Solution space of 2+1 gravity on $\mathbf{R}\times T^2$ in Witten's connection formulation
• The Modular Group, Operator Ordering, and Time in (2+1)-Dimensional Gravity
• Equivalent Quantisations of (2+1)-Dimensional Gravity
• Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions
• Unitary Equivalence of the Metric and Holonomy Formulations of 2+1 Dimensional Quantum Gravity on the Torus
• Six ways to quantize (2+1)-dimensional gravity
• Transition Amplitude in 2+1 dimensional Chern-Simons Gravity on a Torus
• Quantisation of 2+1 gravity for genus 2
• Geometric Structures and Loop Variables in (2+1)-Dimensional Gravity
• Solution to 2+1 Gravity in DreiBein formalism
• Addendum to "Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions"

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