Why does Quantum Electrodynamics Allow a Photon to Exist Temporarily as a Positron and an Electron? In this question...
Why does a photon colliding with an atomic nucleus cause pair production?
...I asked why a photon colliding with a atomic nucleus can become an electron and a positron.  The answer that I thought was most illuminating explained that a photon spends some of its travel time as a particle-antiparticle pair of an electron and a positron. If it strikes the nucleus at the right time, this pair will be separated. It was explained that this is because 'Quantum Electrodynamics allows it'.
Why does Quantum Electrodynamics allow a photon to exist temporarily as an electron and a positron?
 A: It is all hidden in the QED Lagrangian:
One can answer this question in a simple way in terms of the QED Lagrangian, at the electron-field interaction part:
$L=\bar\psi(\partial_\mu\gamma^\mu-m_e+eA_\mu\gamma^\mu)\psi$ 
This tells us that interactions of the form: 
$e^++e^-\rightarrow\gamma$..................(1)
$\gamma\rightarrow e^++e^-$..................(2)
are allowed. This then means that since (1) and (2) are allowed at tree level, at higher order QED the interaction (at one loop level)
$\gamma\rightarrow e^++e^-\rightarrow\gamma$
is also allowed. This is because there is nothing in the fundamental QED Lagrangian, $L$, to tell us that this is not possible. Special relativity as represented by the above Lagrangian allows $E_\gamma=2m_ec^2$ as well as $2mc^2=E_\gamma.$ Quantum mechanics also allows, via the uncertainty principle, for the $e^++e^-$ pair to exist in virtual states, unless some sufficiently strong Coulomb field, or even uniform electric field, or strong gravitational field like just outside a balck hole's event horizon (Hawking radiation) separates them from each other. 
A: If the photon energy $E$ is sufficient to produce a pair ($E>2mc^2$), then a pair can be produced in a collision. It is due to equivalence of mass and energy. The same energy can be "represented" differently - as photons, particles, etc. Kind of conversion of one form of energy into another.
