I am having some problems in evaluating the current problem's question (b)...(adsbygoogle = window.adsbygoogle || []).push({});

I have reached the point (writing only the term which I have problem with):

[itex]A_{3}= - \frac{1}{2} \int_{t_{0}}^{t} dt' dt'' \int d^{3}x \int d^{3}y j(x,t') j(y,t'') D_{F}(x-y)[/itex]

So for some unknown reasons, I cannot see that I can find the Fourier Transform of the classical source to bring it in the needed form...

eg.

[itex] D_{F}= \int \frac{d^{4}p}{(2 \pi)^{4}} \frac{i}{p^{2}-m^{2}} e^{i p (x-y)}[/itex]

[itex]A_{3}=- \frac{1}{2} \int d^{4}x \int d^{4}y j(x) j(y) \int \frac{d^{4}p}{(2 \pi)^{4}} \frac{1}{p^{2}-m^{2}} e^{i p x} e^{-ipy}[/itex]

[itex]A_{3}=- \frac{1}{2} \int \frac{d^{4}p}{(2 \pi)^{4}} \frac{1}{p^{2}-m^{2}} \int d^{4}x j(x) e^{i p x}\int d^{4}y j(y) e^{-ipy}[/itex]

However I don't know how this [itex]p^{0}=E_{p}[/itex] integration can be performed...

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# Peskin & Schroeder Problem 4.1

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