Continuous formulation of the loop quantum gravity phase space

  title={Continuous formulation of the loop quantum gravity phase space},
  author={Laurent Freidel and Marc Geiller and Jonathan Ziprick},
  journal={Classical and Quantum Gravity},
In this paper, we study the discrete classical phase space of loop gravity, which is expressed in terms of the holonomy-flux variables, and show how it is related to the continuous phase space of general relativity. In particular, we prove an isomorphism between the loop gravity discrete phase space and the symplectic reduction of the continuous phase space with respect to a flatness constraint. This gives for the first time a precise relationship between the continuum and holonomy-flux… 
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