 Light-by-light scattering

The elastic scattering of two photons into two photons. In vacuum QED there is no photon self-coupling at tree level; its leading scattering amplitude is the sum of six oriented charged-fermion box diagrams. The superficial degree of divergence is zero, but the photon Ward identities forbid the required local dimension-four $A^4$ counterterm. The complete one-loop Feynman diagram sum is consequently ultraviolet finite. This does not remove its finite four-momentum dependence or its physical thresholds.