# Quantum spin dynamics (QSD): IV. ? Euclidean quantum gravity as a model to test ? Lorentzian quantum gravity

@article{Thiemann1997QuantumSD, title={Quantum spin dynamics (QSD): IV. ? Euclidean quantum gravity as a model to test ? Lorentzian quantum gravity}, author={Thomas Thiemann}, journal={Classical and Quantum Gravity}, year={1997}, volume={15}, pages={1249-1280} }

The quantization of Lorentzian or Euclidean 2 + 1 gravity by canonical methods is a well studied problem. However, the constraints of 2 + 1 gravity are those of a topological field theory and therefore resemble very little those of the corresponding Lorentzian 3 + 1 constraints. In this paper we canonically quantize Euclidean 2 + 1 gravity for an arbitrary genus of the spacelike hypersurface with new, classically equivalent constraints that maximally probe the Lorentzian 3 + 1 situation. We…

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