Calculating & Drawing Feynman Diagrams for $\mathscr{L}$

[PhysicsGente]

Homework Statement

I need to calculate $<\phi(x_1)\phi(x_2)\phi(x_3)>$ and $<\phi(x_1)\phi(x_2)\phi(x_3)>_{c}$ and then draw Feynman diagrams when $\mathscr{L} = -\left(\left(\partial_{\mu}\phi\right)^{2} + m^{2}\phi^{2}\right) - g\phi^{3}$ through first order in $g$.

Homework Equations

$<\phi(x_1)\phi(x_2)\phi(x_3)> = \frac{\delta}{\delta J(x_1)}\frac{\delta}{\delta J(x_2)}\frac{\delta}{\delta J(x_3)}Z[J]|_{J=0}$

$<\phi(x_1)\phi(x_2)\phi(x_3)>_{c} = \frac{\delta}{\delta J(x_1)}\frac{\delta}{\delta J(x_2)}\frac{\delta}{\delta J(x_3)}\ln{(Z[J])}|_{J=0}$

The Attempt at a Solution

I find terms of the form $<\phi(x_1)><\phi(x_2)\phi(x_3)>$ and I'm not sure how to multiply the correlation functions. Any hints on how to do that? Thanks.

I should perhaps say that I know how the diagrams look for $<\phi(x_1)>$ and $<\phi(x_2)\phi(x_3)>$ individually but don't know how to multiply them (or what it means to do that).

ANSWER: You put them together (in one diagram) of course! How silly of me D:

 

[member 553083]

To multiply correlation functions, you just add the diagrams together. For example, if you have two diagrams, one representing <\phi(x_1)> and another one representing <\phi(x_2)\phi(x_3)>, then you can just add them together to get <\phi(x_1)\phi(x_2)\phi(x_3)>. This can be done by connecting the external points of the two diagrams together.