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Homework Help: Complex scalar field propagator

  1. Jan 18, 2013 #1
    i am trying to understand how to express contractions of field operators via propagators.
    we are talking about an interacting theory of 2 complex scalar fields,
    lets call them ψ1 and ψ2.

    the interaction term is: Lint=λ(ψ2)^3(ψ1)

    i have found the free propagator defined as:
    Df-i(x-y)=<0|T(ψi(x) ψi*(y))|0> i=1,2.

    what i am strugling with is that when considering the free parts
    this propagator is 0 for <0|T(ψi ψi)|0> (no complex conjugate=no anti-particle).
    and also it is 0 for <0|T(ψi ψj)|0> ,i≠j.
    meaning that a field can only contract with it's conjugate counter part in the free theory.

    so when i try to calculate an interaction corelator in 1st order of different forms i get 0, for instantce:

    <Ω|T(ψ1 ψ2*)|Ω>
    this term turns out 0 because there is no one to contract with all the none-conjugate fields
    in the interaction hamiltonian.
    am i miss understanding things here,
    or is the first corelator to be none-zero in this picture of the form:
    <Ω|T(ψ2* ψ2* ψ2* ψ1* )|Ω> ??

    help will be much apriciated.
    thank you.
  2. jcsd
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