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Feynman diagrams

  1. Oct 3, 2013 #1
    1. The problem statement, all variables and given/known data

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

    2. Relevant equations

    [itex]<\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}[/itex]

    [itex]<\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}[/itex]

    3. The attempt at a solution

    I find terms of the form [itex]<\phi(x_1)><\phi(x_2)\phi(x_3)>[/itex] 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 [itex]<\phi(x_1)>[/itex] and [itex]<\phi(x_2)\phi(x_3)>[/itex] 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:
    Last edited: Oct 4, 2013
  2. jcsd
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