I read in the book Modern particle physics(page 114-119) from Mark Thomson that for a time-ordered diagram, the energy at each vertex is not conserved, but the momentum is. Furthermore, the energy-momentum relation applies to the intermediate particle X, which is on mass-shell.
On the other hand if we sum over all the Feynman diagrams(which I suppose should be of the same order), then the four-momentum at the vertices is conserved, but now the energy-momentum relation does not apply to the exchanging particle anymore, which is now off mass-shell.
Can anyone please explain why these should be the case? I could not find any explanation in the book except that the energy conservation in the latter case is violated due to the energy-time uncertainty principle - but then again, why can momentum be conserved without regards to the momentum-position uncertainty principle? And why are the exchange particles on mass-shell in the time ordered diagram, but off mass-shell in the sum of all diagrams?
Would be very grateful for clarification on this topic!
Figure 5.4:
Then he states that in a time-ordered diagram energy is not conserved but momentum is
On page 119 he discusses the energy conservation for the sum of all diagrams:
Diagram 5.5:
I have found similar questions here on PSE but there are no answers to those questions as well. Question 1 and Question 2
