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Signicance of positive and negative frequencies?

  1. Sep 11, 2010 #1
    Reading some QFT in which we are faced with inhomogeneous equation

    [tex](\partial^\mu \partial_\mu + m^2)\phi(x)=J(x)[/tex]

    The solution is given as

    [tex]\phi(x)=\phi^{(+)}_{in}(x)+\phi^{(-)}_{out}(x)+i\int{d^4 x\Delta(x-x')J(x')[/tex]

    where [tex]\Delta[/tex] is the appropriate Green's function. "in" means the solution for early times (when J vanishes) and "out" for late times (when J vanishes). The text states "where the superscripts (+) and (-) indicate the positive- and negative-frequency parts, respectively."

    I don't understand why the in- and out-solutions are restricted to the positive- and negative-frequency parts.
  2. jcsd
  3. Oct 25, 2010 #2
    bump. I'm still interested in this. Maybe someone is around now who can look at it.

    Just one little bump. Any insight is appreciated.
  4. Oct 25, 2010 #3


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    The formula is inconsistent with the text. phi plus can't be the solution at early times, because the formula also inlcudes phi minus.

    My recommendation: find a better QFT text.
  5. Oct 25, 2010 #4
    Ok. Thanks.
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