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Wick's Theorem

  1. Feb 17, 2015 #1
    1. The problem statement, all variables and given/known data

    Consider a real free scalar field Φ with mass m. Evaluate the following time-ordered product of field operators using Wick's theorem: ∫d^4x <0| T(Φ(x1)Φ(x2)Φ(x3)Φ(x4)(Φ(x))^4) |0>

    (T denotes time ordering)

    2. Relevant equations

    Wick's theorem: T((Φ(x1)....Φ(xn)) = : (Φ(x1)....Φ(xn)) + all possible contractions :
    ( : ... : denotes normal ordered product)

    3. The attempt at a solution

    I'm really confused here. I've seen examples of using Wick's theorem to evaluate products like T(Φ(x1)Φ(x2)Φ(x3)Φ(x4)) , i.e. field evaluated at fixed values of x only ... but here, there is another term that's integrated over all possible x values. And I have no idea how to deal with that - I've never seen anything like that done in the lectures I've had on this stuff.

    I know contractions of the form "contraction(Φ(x1)Φ(x2))" give Feynman propagators.

    But that's all I've got...

    I'm really bad at this stuff, so if someone can help explain / help me work through this from absolute basics (i.e. assuming I know pretty much nothing), that would be really appreciated!
  2. jcsd
  3. Feb 22, 2015 #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?
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