# Wick's Theorem

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1. Feb 17, 2015

### Naz93

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. Feb 22, 2015