Hamiltonian constraint in Euclidean LQG revisited: First hints of   off-shell Closure
  We initiate the hunt for a definition of Hamiltonian constraint in Euclidean Loop Quantum Gravity (LQG) which faithfully represents quantum Dirac algebra. Borrowing key ideas from previous works on Hamiltonian constraint in LQG and several toy models, we present some evidence that there exists such a continuum Hamiltonian constraint operator which is well defined on a suitable generalization of the Lewandowski-Marolf Habitat and is anomaly free off-shell. 
Alok Laddha
gr-qc hep-th