Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity

@article{Giesel2010AlgebraicQG,
  title={Algebraic quantum gravity (AQG): IV. Reduced phase space quantization of loop quantum gravity},
  author={Kristina Giesel and Thomas Thiemann},
  journal={Classical and Quantum Gravity},
  year={2010},
  volume={27},
  pages={175009}
}
We perform a canonical, reduced phase space quantization of general relativity by loop quantum gravity (LQG) methods. The explicit construction of the reduced phase space is made possible by the combination of (a) the Brown–Kuchař mechanism in the presence of pressure-free dust fields which allows to deparametrize the theory and (b) Rovelli's relational formalism in the extended version developed by Dittrich to construct the algebra of gauge-invariant observables. Since the resulting algebra of… 
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