We develop a scaling theory and a renormalization technique in the context of the modern theory of polarization. The central idea is to use the characteristic function (also known as the polarization amplitude) in place of the free energy in the scaling theory and in place of the Boltzmann probability in a position-space renormalization scheme. We derive a scaling relation between critical exponents which we test in a variety of models in one and two dimensions. We then apply the renormalization to disordered systems. In one dimension, the renormalized disorder strength tends to infinity, indicating the entire absence of extended states. Zero (infinite) disorder is a repulsive (attractive) fixed point. In two and three dimensions, at small system sizes, two additional fixed points appear, both at finite disorder: W a (W r ) is attractive (repulsive) such that W a < W r . In three dimensions, W a tends to zero and W r remains finite, indicating a metal-insulator transition at finite disorder. In two dimensions, we are limited by system size, but we find that both W a and W r decrease significantly as system size is increased.

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