Living Reviews in Relativity

"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
Open References References
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