able to make it work for real . First he could simplify the troublesome by using the identity where is the volume, The first term of the Hamiltonian constraint becomes upon using Thiemann's identity. This Poisson bracket is replaced by a commutator upon quantization. It turns out that a similar trick can be used to teat the second term. Why are the given by the densitized triads ? It actually come about from the Gauss Law We can solve this in much the same way as the Levi-Civita connection can be calculated from the equation ; by rotating the various indices and then adding and subtracting them. The result is complicated and non-linear. To circumvent the problems introduced by this complicated relationship Thiemann first defines the Gauss gauge invariant quantity where , and notes that We are then able to write and as such find an expression in terms of the configuration variable and . We obtain for the second term of the Hamiltonian Why is it easier to quantize ? This is because it can be rewritten in terms of quantities that we already know how to quantize. Specifically can be rewritten as where we have used that the integrated densitized trace of the extrinsic curvature is the "time derivative of the volume". References External links Overview by Carlo Rovelli Thiemann's paper in Physics Letters Good information on LQG Loop quantum gravity