  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, $W_r$ remains finite, indicating 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.
