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QFT free propagator question

  1. Jul 16, 2008 #1
    1. The problem statement, all variables and given/known data

    from Zee QFT in a nutshell

    the free propagator between two "sources" on the field is given by


    [tex] D(x_\mu) = -i \int \frac{d^3k}{(2\pi)^3 2 \omega_k}[e^{-i(\omega_kt-k\bullet x)} \Theta(x_0) + e^{i(\omega_k t-k\bullet x)} \Theta(-x_0) [/tex]

    for a space like separation ([tex] x_0 = 0 [/tex]) Zee gets

    [tex]
    -i\int\frac{d^3k}{(2\pi)^3 2 \omega_k}e^{-i k\bullet x}
    [/tex]

    with assumption that [tex] \Theta(0) = 1/2 [/tex]

    with that assumption i dont agree with Zee i get

    [tex]
    -i\int\frac{d^3k}{(2\pi)^3 2 \omega_k}cos(k \bullet x)
    [/tex]

    where am I going wrong?
     
  2. jcsd
  3. Jul 17, 2008 #2

    Avodyne

    User Avatar
    Science Advisor

    The two expressions are equal. If you write the complex exponential as a sum of a sine and cosine, the sine term will integrate to zero because it is odd in k.
     
  4. Dec 22, 2011 #3
    In the same book, in this definition of the D(x). Why do we get a term exp^-i(ωt-kx) when X_o in positive and a term exp^i(ωt-kx) when X_o is negative?
     
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