Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity

The technique introduced here can also be used to produce a couple of completely well-defined regulated operators including but not exhausting (i) the Euclidean Wheeler-DeWitt operator, (ii) the generator of the Wick rotation transform that maps solutions to the Euclidean Hamiltonian constraint to solutions to the Lorentzian Hamiltonian constraint, (iii) length operators, (iv) Hamiltonian operators of the matter sector and (v) the generators of the asymptotic Poincare group including the quantum ADM energy.