N-point Green's function in QFT

[Dyson]

Hello!
Something about N-point Green's function in QFT really troubles me......
In the path-integral formalism,why will we introduce the N-point Green's function? I mean is it enough because we have calculated the 2-point green's function.
And in the canonical formalism, it seems we can finish the calculation of transition amplitude only with the help of 2-point Green's function(Wick contraction)
What are the differences?

[Dickfore]

What is the equation satisfied by the 2-point Green's function in an interacting field theory?

[Dyson]

Using the pertubative expansion and the definition of N-point Green's function.Because of the pertubation,i can only calculate the 2-point Green's function.But i really can't find the eqution it satisfies.

[Dickfore]

Using the pertubative expansion and the definition of N-point Green's function.Because of the pertubation,i can only calculate the 2-point Green's function.But i really can't find the eqution it satisfies.

Funny, because it carries your name. :)

[CKtalon]

Please correct me if I'm wrong, but when we renormalize the coupling constant, don't you need to calculate the 4point function?

And in calculating the S matrix, you can get some N point function, which has to be reduced to 2 point functions using Wick's contraction, but with all sorts of symmetry factors which you use Feynman diagrams to account for?