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Counting Wick ccontractions

  1. Feb 18, 2015 #1
    Hi guys,

    So basically I'm trying to find the time ordered product:

    [itex]T(:\phi^{3}(x)::\phi^{3}(y):)[/itex]

    for a phi^{3} theory and I'm really having trouble counting the Wick contractions. I've counted the first order contractions which I found to be 9. Second order I got 12 but I dont know if its right, and 3rd order is hopeless. So here's where I'm at so far:

    [itex]T(:\phi^{3}(x)::\phi^{3}(y):)\\
    =:\phi^{3}(x)\phi^{3}(y):+9i\Delta_{F}(x-y):\phi^{2}(x)\phi^{2}(y):+12(i\Delta_{F}(x-y))^{2}:\phi(x)\phi(y): + A(i\Delta_{F}(x-y))^{3}[/itex]

    and I dont know if the factor of 12 is right, or how to find A. I need help!

    Thanks guys!
     
  2. jcsd
  3. Feb 18, 2015 #2
    Okay I think i got A = 6 but no idea lol...:\
     
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