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

[Hluf]

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.

 

[Simon Bridge]

Because that is how you work it out.
Did you have another way in mind?

 

[ChrisVer]

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...