# Applying Wick's Theorem

1. Feb 26, 2010

### vertices

Why is the Feynman diagram for the following nasty 10 point Green's function so simple: I mean it only has two external points, one vertex, and one loop:

Here is the offending function:

$$\int d^4y_1 d^4y_2 <0|T[\phi (x_1) \phi (x_2) \phi^4 (y_1) \phi^4 (y_2)]|0>$$

which I am assuming is simply equal to:

$$\int d^4y_1 d^4y_2 <0|T[\phi (x_1) \phi (x_2) \phi (y_1) \phi (y_1)\phi (y_1) \phi (y_1) \phi (y_2)\phi (y_2) \phi (y_2) \phi (y_2)]|0>$$?

I mean this expression is very complicated - lets see:

$$F(\phi (x_1) \phi (x_2))F(\phi (y_1) \phi (y_1) ) F(\phi (y_1) \phi (y_1) ) F(\phi (y_2) \phi (y_2))F(\phi (y_2) \phi (y_2)) + F(\phi (x_1) \phi (y_1))F( \phi (x_2) \phi (y_1))F(\phi (y_1) \phi (y_1) ) F(\phi (y_2) \phi (y_2))F(\phi (y_2) \phi (y_2)) +....$$

(where F( ) is a contraction of operators).

Is there any way to simply this horrendous expression?

Thanks...

Last edited: Feb 26, 2010