How Can Wick's Theorem Be Applied to Schwinger-Dyson Equations?

[mhill]

in Pages 307-308 of Peskin and Schröeder we find

$$\delta S (< \Omega | T( \phi (x1) \phi(x2)... \phi (xN) | \Omega >)= -\sum_{n=1}^{N}< \Omega | T( \phi (x1) \phi(x2)..i\delta (x-xi)... \phi (xN) | \Omega >$$

they are the Schwinger Dyson equation for the correlation function , my question is , how could i use Wick's theorem to compute the quantity

$$< \Omega | T( \phi (x1) \phi(x2)..i\delta (x-xi)... \phi (xN) | \Omega >$$ for every 'i'

here $$\delta S$$ is the functional derivative of the action 'S'

 

[Avodyne]

Your first equation does not appear in P&S, and I don't understand what you mean by it. Referring to eq.(9.86) on p.307 of P&S, the delta function can be pulled outside the correlation function (since it is just a number, not an operator). Then you are left with a standard correlation function.

 

[zahero_2007]

thatis easy , pull the delta functions out of the correlator and then apply wick's theorm by writing out Green functions"feynman's propagators"