# N-point Correlation Functions

## Main Question or Discussion Point

For a two-point correlation function, it's my understanding we can interpret this as the amplitude for a particle to propagate from one point to another. Is there a similar interpretation for 3- or higher-point correlation functions? When are these used?

Thanks!

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They are used when calculating the scattering cross sections.

For a two-point correlation function, it's my understanding we can interpret this as the amplitude for a particle to propagate from one point to another. Is there a similar interpretation for 3- or higher-point correlation functions? When are these used?
you can always contract one field to another one, not in adjacent to the first one and you still have a green function.You can contract any two and the result for contracting is the green function multiplied by other operator that remained.For example if you have
<0|T{ψ1ψ2ψ3ψ4)|0> then you will have GF(1-2)GF(3-4)+....,where ... is for other two choices.Those operator which are not contracted gives zero.You will not have an odd term like 3 point because that will give zero(contract with who).So you can still apply the interpreatation you want,for particle being created at 1, destroyed at 2 and particle created at 3 ,destroyed at 4.You can create diagrams using these,called feynman diagrams.Some of these diagrams will be disconnected ,you just leave them.you can use these diagram to calculate amplitude.

As I understand it the name 2,3,4... correlation function is coming from how many particles you have (or they call them external point in the Feynman diagrams). In the 2-point function you have 2 external fields at lets say space points x1 and x2. You can connect them by a line and that is it - the propagator. With 4-point function you have 4 points, You are connecting them 2 by 2 (this is the Wick contraction) in many ways now. For example you can have two electrons entering, two going out, no interaction (the lines do not cross) and the probability for this process is in the 4-point function. But you can have them interacting with each other (the lines now cross) and this is also contributing to the 4-point function. So in other words if you want to calculate scattering of 2 particles this is a 4-point function. As I imagine it n-point will be n particles scattering. I cannot imagine 3-point function that is not a fully disconnected one (when you connect each point to the other two, kind of a triangle shape) but those are part of the energy expectation of the vacuum and are zero at the end. So it is for all odd numbered correlation functions.