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Currently reading through Robert Klauber's Student Friendly Quantum Field Theory and he got me wondering about electron-positron annihilation.

In Chapter 8 he goes over the expansion of the S-Operator. He uses examples like Bhabha scattering, which includes a second-order diagram for electron/positron annihilation, showing an incoming electron/positron pair annihilating and producing a virtual photon followed by creation of another pair of outgoing electron/positron pair.

Here's my current hang-up: In the expansion of the S-operator, he demonstrates that 1-vertex interactions are NOT physical, which seems to mean an electron/positron pair CANNOT annihilate to produce a real photon.

Does that mean all physically realizable electron/positron pair annihilation MUST be followed by another pair being created?

Otherwise it's a 1-vertex interaction, right?

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    $\begingroup$ No, because electron/positron pairs can annihilate to more than one photon. $\endgroup$
    – Luke Pritchett
    Commented Jul 3, 2017 at 17:48

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No, an electron and position can also realistically annihilate into two real photons via this second-order scattering process (where time runs downward in the diagram):

enter image description here

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  • $\begingroup$ Ahh, simple enough! Thanks @tparker, I wasn't aware of this interaction. $\endgroup$
    – EthanT
    Commented Jul 3, 2017 at 17:56

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