A Phase Space Path Integral for (2+1)-Dimensional Gravity

Abstract

I investigate the relationship between the phase space path integral in (2+1)-dimensional gravity and the canonical quantization of the corresponding reduced phase space in the York time slicing. I demonstrate the equivalence of these two approaches, and discuss some subtleties in the definition of the path integral necessary to prove this equivalence.

9 pages, LaTeX, no figures. (Minor changes, in particular to clarify exceptional features of torus topology; final version to appear in Class. Quant. Grav.)

References in corpus (8)

• Gauge Invariance for Generally Covariant Systems
• The Sum over Topologies in Three-Dimensional Euclidean Quantum Gravity
• Solution space of 2+1 gravity on $\mathbf{R}\times T^2$ in Witten's connection formulation
• Topology Change in (2+1)-Dimensional Gravity
• Entropy vs. Action in the (2+1)-Dimensional Hartle-Hawking Wave Function
• Quantum gravitational measure for three-geometries
• QUANTUM ASPECTS OF 2+1 GRAVITY
• Topology change in ISO(2,1) Chern-Simons gravity

Cited by in corpus (9)

• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Loop Quantum Gravity a la Aharonov-Bohm
• Quantum Minimal Length and Transplanckian Photons
• Quantum algebra of the Hamiltonian constraint in reduced four-dimensional gravity
• Back-Reaction on the Topological Degrees of Freedom in (2+1)-Dimensional Spacetime
• Functional approach to 2+1 dimensional gravity coupled to particles
• Noncritical M-theory: Three Dimensions
• Partition Function for (2+1)-Dimensional Einstein Gravity
• Quantum Gravity at Very High Energies