I have read on the Principle of locality Wikipedia page that:
"The special theory of relativity limits the speed at which all such influences can travel to the speed of light, c. Therefore, the principle of locality implies that an event at one point cannot cause a simultaneous result at another point."
But this has no "use" for me in scattering amplitude physics, so I looked more into it and, in a question on this website, I found this talk. What I understood from it was that locality implies conservation of momentum:
$$\sum p_i =0$$
Is this correct?
If so is it all I need to know about the concept of locality for scattering amplitudes, or is there another mathematical meaning behind it?