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A Free theory time-ordered correlation functions with derivatives of fields

  1. Nov 18, 2016 #1
    Consider the following time-ordered correlation function:

    $$\langle 0 | T \{ \phi(x_{1}) \phi(x_{2}) \phi(x) \partial^{\mu}\phi(x) \partial_{\mu}\phi(x) \phi(y) \partial^{\nu}\phi(y) \partial_{\nu}\phi(y) \} | 0 \rangle.$$

    The derivatives can be taken out the correlation function to give

    $$\partial^{\mu'}\partial_{\mu''}\partial^{\nu'}\partial_{\nu''}\langle 0 | T \{ \phi(x_{1}) \phi(x_{2}) \phi(x''') \phi(x') \phi(x'') \phi(y''') \phi(y') \phi(y'') \} | 0 \rangle.$$

    There are six distinguishable field points in the correlation function:

    $$\phi(x_{1})\qquad\phi(x_{2})\qquad\phi(x''')\qquad\phi(x')\qquad\phi(y''')\qquad\phi(y').$$

    ##\phi(x')## and ##\phi(x'')## are not distinguishable because the derivative operator acts on both of these fields. Same goes for ##\phi(y')## and ##\phi(y'')##.

    How many different Feyman diagrams exist for this time-ordered correlation function?
     
  2. jcsd
  3. Nov 23, 2016 #2
    Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
     
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