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Time-ordered product of real scalar fields

  1. Feb 17, 2015 #1
    Hi guys,

    So I've got a real scalar field which is the sum of the positive frequency part and negative frequency part:

    [itex]\phi(x)=\phi^{(+)}(x)+\phi^{(-)}(y)[/itex]

    and I'm looking at the time-ordered product:

    [itex]T(\phi(x)\phi(y))=\theta(x^{0}-y^{0})\phi(x)\phi(y)+\theta(y^{0}-x^{0})\phi(y)\phi(x)[/itex]

    for the two cases where [itex]x^{0}>y^{0}[/itex] and [itex]x^{0}<y^{0}[/itex]. So in the first case:

    [itex]T(\phi(x)\phi(y))=:\phi(x)\phi(y):+[\phi^{(+)}(x),\phi^{(-)}(y)][/itex], that's all good.

    However for the second case, here is what my lecturer has written:

    [itex]T(\phi(x)\phi(y))=:\phi(x)\phi(y):+\theta(x^{0}-y^{0})<0|\phi(x)\phi(y)|0>+\theta(y^{0}-x^{0})<0|\phi(y)\phi(x)|0>[/itex].

    I have no idea how/why all of a sudden the expectation value is being taken using the vacuum states. Can someone please explain, why is this so different from the first case?
     
  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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