Of course ``quantization'' is far from a univocal algorithm, particularly for a nonlinear field theory. Rather, it is a poorly understood inverse problem (find a quantum theory with the given classical limit). More or less subtle choices are made in constructing the quantum theory. I discuss these choices below.

- 5.1 Quantum field theory on a differentiable manifold
- 5.2 One additional assumption
- 5.3 Physical meaning of diffeomorphism invariance, and its implementation in the quantum theory
- 5.4 Problems not addressed

Loop Quantum Gravity
Carlo Rovelli
http://www.livingreviews.org/lrr-1998-1
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