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A Free theory time-ordered correlation function with two internal fields

  1. Nov 19, 2016 #1
    Wick's theorem allows one to write a free theory time-ordered ##n##-point correlation function as a product of free theory time-ordered ##2##-point correlation function.

    The procedure involves the pairwise Wick contraction of fields such that external fields are not paired up each other.


    Consider the following time-ordered correlation function:

    $$\langle 0 | T \{ \phi(x_{1}) \phi(x_{2}) \phi(x) \phi(x) \phi(x) \phi(y) \phi(y) \phi(y) \} | 0 \rangle.$$

    This time-ordered ##8##-point correlation function can be Wick contracted in multiple ways.

    1. One possible Wick contraction pairs ##\phi(x_{1})## with one ##\phi(x)## and pairs ##\phi(x_{2})## with another ##\phi(x)##.

    2. Another possible Wick contraction pairs ##\phi(x_{1})## with one ##\phi(x)## and pairs ##\phi(x_{2})## with one ##\phi(y)##.

    3. A third possible Wick contraction pairs ##\phi(x_{1})## with one ##\phi(y)## and pairs ##\phi(x_{2})## with another ##\phi(y)##. However, this appears to be redundant as it is already covered in the first choice of Wick contractions. Am I wrong?
     
  2. jcsd
  3. Nov 24, 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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