Recently I started a new thread regarding Gribov (gauge fixing) ambiguities in quantum field theory, especially in QCD https://www.physicsforums.com/showthread.php?t=429759. Of course every theory incorporating a local gauge symmetry may have this gauge fixing issue - therefore in GR and all approaches towards a theory of quantum gravity the same problem should arise. Has anybody seen something like gauge fixing ambiguities in LQG (the method is totally different from QFT, therefore I cannot even say where to look for these issues), in asymptotic safety (there is an overcounting of metrics which is not gauge but diffeo - perhaps the same applies here) or any other aproach towards QG? If these gauge fixing ambiguities can be avoided, why isn't this possible in non-abelian QFTs? Rearding LQG it seems to be related to the loops which are gauge invariant. The non-separable Hilbert space can be reduced via the diffeo-constraint - which is not available in QFTs; is this the main difference?