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Time ordering operator, interaction Lagrangian, QED

  1. Dec 19, 2014 #1
    1. The problem statement, all variables and given/known data
    I am trying to calculate the following quantity:
    $$<0|T\{\phi^\dagger(x_1) \phi(x_2) exp[i\int{L_1(x)dx}]\}|0>$$


    $$ L_1(x) = -ieA_{\mu}[\phi^*
    (\partial_\mu \phi ) - (\partial_\mu \phi^*)\phi] $$

    I am trying to find an expression including the propagators, wick's theorem, and then calculate the Feynman diagrams in position space.
    The solution should include terms of up to ## e^2 ## order.

    2. Relevant equations

    3. The attempt at a solution
    I am not sure if the Lagrangian ## L_1(x) ## is the interaction Lagrangian, so that I should use it as it is in the integral, or if I should extract an interaction Lagrangian out of it.
    I also have to tell you that I am not expected to calculate complex integrals in every detail, or be occupied with infinities.
  2. jcsd
  3. Dec 24, 2014 #2
    Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?
  4. Dec 29, 2014 #3


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    Gold Member

    Look in your problem statement. It says "where L1(x) = ... " and L1(x) is what appears in the integral.

    As to solving the problem: Look up the properties of the time-ordering operator and the nature of the <0| and |0> . There are operations you can perform on the T operator to simplify your expression. Your text should give you some examples of what I am talking about.
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