Loop quantum gravity without the Hamiltonian constraint

  title={Loop quantum gravity without the Hamiltonian constraint},
  author={Norbert Bodendorfer and Alexander Stottmeister and Andreas Thurn},
  journal={Classical and Quantum Gravity},
We show that under certain technical assumptions, including the existence of a constant mean curvature (CMC) slice and strict positivity of the scalar field, general relativity conformally coupled to a scalar field can be quantized on a partially reduced phase space, meaning reduced only with respect to the Hamiltonian constraint and a proper gauge fixing. More precisely, we introduce, in close analogy to shape dynamics, the generator of a local conformal transformation acting on both, the… 
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