The annihilation (or decay) of an electron-positron pair into a single photon, e+ + e- ? ?, cannot occur because energy and momentum would not be conserved in this process. The reverse reaction is also impossible for this reason, except in the presence of another particle that can carry away the excess energy and momentum. However, in quantum field theory this process is allowed as an intermediate quantum state. Some authors justify this by saying that the photon exists for a time which is short enough that the violation of energy conservation can be accommodated by the uncertainty principle. Others choose to assign the intermediate photon a non-zero mass. (The mathematics of the theory are unaffected by which view is taken.) This opens the way for virtual pair production or annihilation in which a one-particle quantum state may fluctuate into a two-particle state and back again. These processes are important in the vacuum state and renormalization of a quantum field theory. It also allows neutral particle mixing through processes such as the one pictured here.
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