Reading some QFT in which we are faced with inhomogeneous equation(adsbygoogle = window.adsbygoogle || []).push({});

[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.

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# Signicance of positive and negative frequencies?

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