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?
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The theorem you've linked to is true - in vacuum.
SPDC happens in a non-linear medium which breaks the symmetries that underlie the hypotheses of that theorem. As such, there is no contradiction between the two.
Emilio Pisanty
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