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Is it possible to have a Feynman diagram with 3 vertices for process involving 2 initial particles and 2 final particles? For example, for the scattering of a fermion and anti-fermion in the Yukawa theory $\psi \overline{\psi} \rightarrow \psi \overline{\psi}$ where the interaction term is $\phi \psi \overline{\psi}$

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You could have for example the following $\psi \bar{\psi} \to \psi \bar{\psi}$ diagram, where there is one fermion propagator and one fermion propagator with a loop.

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  • $\begingroup$ You mean something like this for example ? imgur.com/a/0vO3I What would be the physical interpretation of the loop ? The lepton emits and absorb the particle at the same space time point ? $\endgroup$ – Samuel Mar 7 '17 at 14:00
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    $\begingroup$ Yes, that diagram is also possible. Feynman diagrams are terms in a perturbations series to calculate correlation functions. There is no particular physical interpretation of a single diagram (though people in popular explanations unfortunately often pretend there is). $\endgroup$ – JgL Mar 7 '17 at 15:49

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