Are the spectra of geometrical operators in Loop Quantum Gravity really discrete

@article{Dittrich2009AreTS,
  title={Are the spectra of geometrical operators in Loop Quantum Gravity really discrete},
  author={Bianca Dittrich and Thomas Thiemann},
  journal={Journal of Mathematical Physics},
  year={2009},
  volume={50},
  pages={012503-012503}
}
One of the celebrated results of Loop Quantum Gravity (LQG) is the discreteness of the spectrum of geometrical operators such as length, area and volume operators. This is an indication that Planck scale geometry in LQG is discontinuous rather than smooth. However, there is no rigorous proof thereof at present, because the afore mentioned operators are not gauge invariant, they do not commute with the quantum constraints. The relational formalism in the incarnation of Rovelli’s partial and… 

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