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

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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