Addendum to "Classical and Quantum Evolutions of the de Sitter and the anti-de Sitter Universes in 2+1 dimensions"

Abstract

The previous discussion \cite{ezawa} on reducing the phase space of the first order Einstein gravity in 2+1 dimensions is reconsidered. We construct a \lq\lq correct" physical phase space in the case of positive cosmological constant, taking into account the geometrical feature of SO(3,1) connections. A parametrization which unifies the two sectors of the physical phase space is also given.

Latex 8 pages (Crucial and essential changes have been made.)

References in corpus (4)

• (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
• 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

Cited by in corpus (7)

• Ponzano-Regge model revisited I: Gauge fixing, observables and interacting spinning particles
• Quantum Gravity in 2+1 Dimensions: The Case of a Closed Universe
• Comparative Quantizations of (2+1)-Dimensional Gravity
• Chern-Simons Quantization of (2+1)-Anti-De Sitter Gravity on a Torus
• QUANTUM ASPECTS OF 2+1 GRAVITY
• The Torus Universe in the Polygon Approach to 2+1-Dimensional Gravity
• A semiclassical interpretation of the topological solutions for canonical quantum gravity