Time ordering operator, interaction Lagrangian, QED

In summary, the problem statement involves calculating a quantity using the time-ordering operator and a Lagrangian function. The solution should include terms up to second order in the coupling constant. To simplify the expression, one can use properties of the time-ordering operator and the nature of the initial and final states.
  • #1
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Homework Statement


I am trying to calculate the following quantity:
$$<0|T\{\phi^\dagger(x_1) \phi(x_2) exp[i\int{L_1(x)dx}]\}|0>$$

where:

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

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.

Homework Equations




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.
[/B]
 
  • #3
askalot said:
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,

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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