In a Feynman diagram, the particles behave like free particles everywhere except at one of the vertex of the diagram. The vertex is the site for an interaction to occur.
So, if we have an electron which emits and later absorbs the same photon, we already have 2 vertex in the diagram. But i think that a third vertex is necessary for the electron to change its direction of motion and catch up with the photon.
This is because being free particles, after emission, the electron and the photon will keep on moving away from each other. So, we need a third vertex to scatter the electron and help it catch up with the virtual photon. If the photon returns on its own, this will violate the law of conservation of momentum.
But the funny thing is- I have seen Feynman himself draw the Feynman diagram i describe with just 2 vertex in a QED lecture video.
So, do i have some misconceptions regarding Feynman diagrams? Please help!