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Applying Wick's Theorem

  1. Feb 26, 2010 #1
    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:

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

    which I am assuming is simply equal to:

    [tex]\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>[/tex]?

    I mean this expression is very complicated - lets see:

    [tex]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)) +.... [/tex]

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

    Is there any way to simply this horrendous expression?

    Last edited: Feb 26, 2010
  2. jcsd
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