How to Count Wick Contractions in Phi^3 Theory?

  • Thread starter Dixanadu
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Dixanadu
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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 don't 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 don't know if the factor of 12 is right, or how to find A. I need help!

Thanks guys!
 
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  • #2
Okay I think i got A = 6 but no idea lol...:\
 

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