  We derive a formula for the electric polarization of interacting insulators,
expressed in terms of the full Green's and vertex functions. We exemplify this
method in the half-filled ionic Hubbard model treated within dynamical mean
field theory (DMFT). The electric polarization of a correlated band insulator
is determined by the interplay of ionicity and covalency, and both quantities
are renormalized by the electron-electron interactions. We introduce
quasiparticle approximation to the exact equation for the polarization, and
compare the results of this approximation with those of the exact DMFT
formulation and of static mean field theories such as the LDA+ U. The latter
overestimates the electronic contribution to the electric polarization when the
quasiparticle weight of the active bands is very small.
