On the low-energy limit of the QED N-photon amplitudes

We derive an explicit formula for the low energy limits of the one-loop on-shell massive N-photon amplitudes, for arbitrary N and all helicity assignments, in scalar and spinor QED. The two-loop corrections to the same amplitudes are obtained for up to the ten point case. All photon amplitudes with an odd number of '+' helicities are shown to vanish in this limit to all loop orders