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I'm new to particle physics, and I'm reading chapter 5 of Prof. Mark A. Thompson's "Modern Particle Physics", which talks about Time-ordered perturbation theory vs QED. However, in page 119 he wrote:

By expressing the interaction in terms of the exchange of a virtual particle with four-momentum $q$, both momentum and energy are conserved at the interaction vertices of a Feynman diagram. This is not the case for the individual time-ordered diagrams, where energy is not conserved at a vertex

The same thing is mentioned in the slides accompanying this chapter, at page 6. My question is: how exactly is energy not conserved in the vertices of the 2 diagrams? And shouldn't this be a red flag, considering that the exchanging particles are "on mass-shell" (meaning they are physical? I'm not entirely sure yet).

Thank you!

Book: enter image description here

Slide: enter image description here

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    $\begingroup$ I think the need for a sum to end up with the usual feynman diagram, as seen in the last part of the copy, gives a clue . It is feynman diagrams that give the correct calculations. I also am waiting for a clear answer to this. $\endgroup$ – anna v Oct 22 '18 at 18:16

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