  We compute finite volume effects relevant for lattice QCD simulations using
background fields. Focusing on constant electric and magnetic fields on a
periodic lattice, we determine volume corrections to pion two-point functions
using chiral perturbation theory. Among such corrections are the finite volume
shifts to the electric and magnetic polarizabilities, which are numerically
shown to be non-negligible. We additionally find that all terms in the
single-particle effective action can be renormalized by infrared effects. This
includes Born couplings to the pion current and total charge-squared, which can
be renormalized due to the nature of gauge invariance on a torus.
