QUANTUM ASPECTS OF 2+1 GRAVITY

Abstract

We review and systematize recent attempts to canonically quantize general relativity in 2+1 dimensions, defined on space-times $\mathbb{R}\times {\Sigma }^g$, where ${\Sigma }^g$ is a compact Riemann surface of genus $g$. The emphasis is on quantizations of the classical connection formulation, which use Wilson loops as their basic observables, but also results from the ADM formulation are summarized. We evaluate the progress and discuss the possible quantum (in)equivalence of the various approaches.

24 pages, TeX, Mar 95; contribution to the JMP special issue on "Quantum geometry and diffeomorphism invariant quantum field theory"

References in corpus (19)

• (2+1)-Dimensional Chern-Simons Gravity as a Dirac Square Root
• Solution space of 2+1 gravity on $\mathbf{R}\times T^2$ in Witten's connection formulation
• Invariants of 2+1 Quantum Gravity
• Comparative Quantizations of (2+1)-Dimensional Gravity
• Loop Representations for 2+1 Gravity on a Torus
• New Loop Representations for 2+1 Gravity
• The Modular Group, Operator Ordering, and Time in (2+1)-Dimensional Gravity
• Notes on the (2+1)-Dimensional Wheeler-DeWitt Equation
• 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
• Completeness of Wilson loop functionals on the moduli space of $SL(2,C)$ and $SU(1,1)$-connections
• Large Diffeomorphisms in (2+1)-Quantum Gravity on the Torus
• Loop Variable Inequalities in Gravity and Gauge Theory
• Chern-Simons Quantization of (2+1)-Anti-De Sitter Gravity on a Torus
• Quantisation of 2+1 gravity for genus 2
• Ashtekar Formulation of 2+1 Gravity on a Torus
• Chromodynamics and Gravity as Theories on Loop Space
• Addendum to "Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions"
• Independent Loop Invariants for 2+1 Gravity

Cited by in corpus (10)

• Time Dependence of Hawking Radiation Entropy
• Three Dimensional Black Hole Coupled to the Born-Infeld Electrodynamics
• Non-perturbative 3d Lorentzian Quantum Gravity
• Discrete Lorentzian Quantum Gravity
• Fuzzy spacetime from a null-surface version of GR
• A Phase Space Path Integral for (2+1)-Dimensional Gravity
• Group-Theoretical Quantization of 2+1 Geavity in the Metric-Torus Sector
• In Search of Fundamental Discreteness in 2+1 Dimensional Quantum Gravity
• Partition Function for (2+1)-Dimensional Einstein Gravity
• Gravitational interpretation of the Hitchin equations