  We use chiral perturbation theory to study the extraction of pion
electromagnetic polarizabilities from lattice QCD. Chiral extrapolation
formulae are derived for partially quenched QCD, and quenched QCD simulations.
On a torus, volume dependence of electromagnetic observables is complicated by
SO(4) breaking, as well as photon zero-mode interactions. We determine finite
volume corrections to the Compton scattering tensor of pions. We argue,
however, that such results cannot be used to ascertain volume corrections to
polarizabilities determined in lattice QCD with background field methods.
Connection is lacking because momentum expansions are not permitted in finite
volume. Our argument also applies to form factors. Volume effects for
electromagnetic moments cannot be deduced from finite volume form factors.
