Scattering of Light by Light

In 1936, well before the invention of quantum electrodynamics (QED), Heisenberg and his student Euler wrote an effective classical Lagrangian for light-light interaction (non-linear optics!) based on quantum mechanical modifications of E&M and Dirac's wave equation. In my talk, I will explain how the non-linearity of low-energy light-light interactions can be seen from QED. Important concepts like renormalization will be discussed, and I will end with recent proposals for experiments that measure this (very small) effect.