An ingredient in recent discussions of curvature singularity avoidance in quantum gravity is the “inverse scale factor” operator in quantum cosmology, and its generalizations to field theoretic models such as scalar-field collapse in spherical symmetry. I describe a general lattice origin of this idea, and show how it applies to the Coulomb singularity in quantum mechanics. The example demonstrates that a discretized Schrodinger equation is computationally equivalent to the so-called polymer quantization derived loop quantum gravity. This applies also to lattice discretized forms of the Wheeler–deWitt equation.PACS Nos.: 04.60.–m, 04.60.Ds, 04.70.Dy
Gravity quantized: Loop quantum gravity with a scalar field
