Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A confusion from David tong's notes on QFT

  1. Jan 29, 2011 #1
  2. jcsd
  3. Jan 29, 2011 #2
    He didn't just insert |0><0|. He's applying Wick's theorem, and his contractions correlations in the |0> state.
  4. Jan 30, 2011 #3
    It's already normal ordered, so I don't think he applied Wick's theorem. And I still don't see why we can insert |0><0|.
  5. Jan 30, 2011 #4
    I just took a quick look and I'm not sure about his conventions, but from the conventions I'm used to here is my reasoning:

    The expression [tex] : \psi_1^\dagger \psi_1 \psi_2^\dagger \psi_2 : [/tex] is normal ordered. So in any terms in the creation/annihilation-operator expansion of this, all annihilation operators act on the state to the right before any creation operators do.

    Since the incoming state on the right contains two particles and no anti-particles, the only contribution from this comes from terms where there are two particle annihilation operators (no anti-particle annihilation operators). This comes only from the [tex] \psi [/tex], not the [tex] \psi^\dagger[/tex].

    The only possible result from the particle annihilation operators acting on the right is the vacuum state. Therefore he can factorize as he does, and put in |0><0| in the middle.
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Similar Discussions: A confusion from David tong's notes on QFT