"Quantum Gravity in 2+1 Dimensions:
The Case of a Closed Universe"
by
Steven Carlip
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Abstract
1
Introduction
2
Classical Gravity in 2+1 Dimensions
2.1
Why (2+ 1)-dimensional gravity is simple
2.2
Geometric structures
2.3
The Chern-Simons formulation
2.4
The ADM approach
2.5
Exact discrete approaches
2.6
Large diffeomorphisms
2.7
The torus universe
2.8
Dynamics
3
Quantum Gravity in 2+1 Dimensions
3.1
Reduced phase space quantization
3.2
Chern-Simons quantization
3.3
Covariant canonical quantization
3.4
A digression: Observables and the problem of time
3.5
“Quantum geometry”
3.6
Lattice methods I: Ponzano-Regge and spin foams
3.7
Lattice methods II: Dynamical triangulations
3.8
Other lattice approaches
3.9
The Wheeler-DeWitt equation
3.10
Lorentzian path integrals
3.11
Euclidean path integrals and quantum cosmology
4
What Have We Learned?
5
What Can We Still Learn?
6
Acknowledgments
References
Figures