Why do we integrate over the relative momentum of interacting particles?

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SUMMARY

The integration over the relative momentum of interacting particles is essential for accurately calculating the amplitude of their interactions. This method involves integrating over the propagator momentum transfer, denoted as q, which can assume any value. By performing this integration, one accounts for all possible momentum configurations that contribute to the interaction. This approach is fundamental in quantum field theory and particle physics.

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Hluf
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When we describe the amplitude of two interacting particles, we are integrating w.r.t the relative momentum of the particles. Why we do this?
Thank you all of you.
 
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Because that is how you work it out.
Did you have another way in mind?
 
Because you integrate over the propagator momentum transfer... the propagator will propagate the momentum from one particle to the other, but its momentum transfer q can take any value...
So you integrate over it to take all possible momenta??
Maybe I;m wrong, without seeing the actual formula...
 

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