# Furry's theorem and spontaneous parametric down-conversion

In spontaneous parametric down-conversion, a single photon interacts with a nonlinear medium to produce a pair of lower energy photons. It is observed that energy, momentum, and orbital-angular-momentum are conserved in the process. However, I have seen arguments invoking Furry's theorem (see https://www.maths.tcd.ie/~fionn/qft/furry.pdf) stating that it is not possible for a photon to get destroyed to produce two photons. What is the key insight that I am missing here?

• Unless the medium is a positronium crystal, or something similar, then it certainly does not possess charge-conjugation symmetry. (Hint: if it has electrons but it doesn't have positrons, then it's $C$-asymmetric.) But that's not really necessary - the lack of inversion symmetry is sufficient. – Emilio Pisanty Jan 24 '19 at 11:09