See the Breit-Wheeler process, wherein two gamma photons are converted into an electron and a positron via a process that's the reverse of electron-positron annihilation. I do not doubt this process. However I'm less confident about the Wikipedia two-photon physics article. It talks about gamma-gamma pair production, and as far as I know it's in line with what some particle physicists say. It says this:
"From quantum electrodynamics it can be found that photons cannot couple directly to each other, since they carry no charge, but they can interact through higher-order processes[clarification needed]. A photon can, within the bounds of the uncertainty principle, fluctuate into a charged fermion–antifermion pair, to either of which the other photon can couple".
However as far as I know, a 511keV photon does not spend its life magically morphing into a 511keV electron and a 511keV positron. That’s in breach of conservation of energy. In similar vein the electron and the positron cannot then magically morph back into a single 511keV photon. That's in breach of conservation of momentum. Moreover photons travel at the speed of light whilst electrons and positrons do not – a photon cannot spend its life fluctuating into fermion pairs, if it did it couldn't travel at c. Besides, virtual particles are virtual. As in not real. They aren't short-lived real particles that pop in and out of existence like magic. Instead they only exist in the mathematics of the model. Which is why hydrogen atoms don’t twinkle, and magnets don’t shine. On top of all that pair production surely does not occur because pair production occurred. Spontaneously. Like worms from mud. All in all, this explanation for pair production is woefully inadequate. A better explanation is required. So:
How does gamma-gamma pair production really work?
I will give a 500-point bounty to the least-worst answer to the question. One answer will get the bounty, even if I don't like it.
Best Answer
Quantum field theory does not offer a description of "how" its processes work, just like Newtonian mechanics doesn't offer an explanation of "how" forces impart acceleration or general relativity an explanation of "how" the spacetime metric obeys the Einstein equations.
The predictions of quantum field theory, and quantum electrodynamics (QED) in particular, are well-tested. Given two photons of sufficient energy to yield at least the rest mass of an electron-positron pair, one finds that QED predicts a non-zero amplitude for the process $\gamma\gamma \to e^+ e^-$ to happen. That is all the theory tells us. No "fluctuation", no "virtual particles", nothing. Just a cold, hard, quantitative prediction of how likely such an event is.
All other things - for instance the laughable description in the Wikipedia article you quote - are stories, in this case a human-readable interpretation of the Feynman diagrams used to compute the probability of the event, but should not be taken as the actual statement the quantitative theory makes.
There is no "how", what happens between the input and the output of a quantum field theoretic process is a black box called "time evolution" that has no direct, human-readable interpretation. If we resolve it perturbatively with Feynman diagrams, people like to tell stories of virtual particles, but no one forces us to do that - one may organize the series in another way, may be even forced to do so (e.g. at strong coupling), or one may not use a series at all to compute the probability. The only non-approximative answer to "how" the scattering processes happen in quantum field theory that QFT has to offer is to sit down and derive the LSZ formula for scattering amplitudes from scratch, as it is done in most QFT books. Which, as you may already see from the Wikipedia article, is not what passes as a good story in most circles.
But neither nature nor our models of it are required to yield good stories. Our models are required to yield accurate predictions, and that is what quantum field theory does.