Volume effects for pion two-point functions in constant electric and magnetic fields

We compute finite volume effects relevant for lattice QCD simulations using quantized 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.