# "Mirrored" diagrams of $n$-point functions

Suppose we are calculating the two-point function $$\langle\phi(x_1)\phi(x_2) \rangle$$ and we've obtained a loop diagram of the kind on the left. Will there necessarily also be a diagram as on the right? Or is this part of the symmetry of the one on the left? I know in correlation function calculations that the external lines of the diagrams are fixed, so we don't take them into account in calculating the symmetry factor.

I hope this is the last question I have on this matter :)

The 2 external legs on the two-point function $$\langle\phi(x_1)\phi(x_2) \rangle$$ carry distinguishable labels $$x_1$$ and $$x_2$$, so there is no symmetry between the 2 external legs. And hence OP's 2 above diagrams are different.
• I assume the same holds for 3 point functions then too. But won't that give you $3! = 6$ graphs per configuration? Or is this not the case? Could you maybe work out a small example to illustrate? For example imgur.com/a/VRcJB0t Commented Mar 27, 2023 at 9:24