# Counting Wick ccontractions

1. Feb 18, 2015

Hi guys,

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

$T(:\phi^{3}(x)::\phi^{3}(y):)$

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:

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

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

Thanks guys!

2. Feb 18, 2015