What is the interpretation of $n$-point Green's functions, for $n>2$?

Question

Disclaimer: I am not a Physicist. So please correct any misunderstanding that I may have.

From what I understand, a $2$-point Green function can be interpreted as the response at $x_2$, when you have a delta function source at point $x_1$. Is there a similar interpretation for $n$-point Green's functions, as in QFT for instance? I know they are defined as vacuum expectation values of a product of $n$-operators, possibly ordered in some way, but I don't understand how to relate the definition, with the much simpler description above.

Can anyone please clear my confusion?

Answer 1

The $n$-point correlation function has an analogous interpretation to the 2-point correlation function: it gives the probability amplitude ('response') for finding some number $n-p$ of (delta function-shaped) particles at positions $x_{(p+1)}..x_n$, starting from $p$ (delta function-shaped) particles at initial positions $x_1..x_p$.

Here, the number $p$ does not really matter: mathematically, we are only associating some amplitude to a configuration of $n$ delta-function sources, and the split in $p$ and $n-p$ sources is arbitrary.