The three photon vertex

Owing to weak interactions, the three-photon vertex is non-zero. From gauge invariance and symmetry requirements, it is shown that the C=-1P=-1 vertex amplitudes are at least of order q⁷ in the limit of soft photon momentum q and that if any two photons are placed on mass shell the form factors vanish identically. To lowest order in q the effective current is in fact given by j_rho=b epsilon _{kappa lambda mu nu} ( delta ²(F^{kappa lambda} delta _rhoF^{mu nu})- delta _rho(F^{kappa lambda} delta ²F^{mu nu})). b is estimated in certain models of weak interactions.