This is probably really simple. In chapter I.4 the jump from (4) -> (5) is sort of eluding(adsbygoogle = window.adsbygoogle || []).push({});

[tex] W(J) = - \iint dx^0 dy^0 \int \frac{dk^0}{2\pi} e^{i k^0(x - y)^0} \int \frac{d^3k}{(2 \pi)^3} \frac{e^{i \vec{k}(\vec{x_1} - \vec{x_2})}} {k^2 - m^2 + i\epsilon} [/tex]

and

[tex] \omega^2 = \vec{k}^2 + m^2 [/tex]

He got

[tex] W(J) = \int dx^0 \int \frac{d^3k}{(2\pi)^3} \frac{e^{i \vec{k} (\vec{x_1} - \vec{x_2})}}{\vec{k}^2 + m^2} [/tex]

the way I see it - the middle term is the delta function

[tex] W(J) = - \iint dx^0 dy^0 \delta(x^0 - y^0) \int \frac{d^3k}{(2 \pi)^3} \frac{e^{i \vec{k}(\vec{x_1} - \vec{x_2})}} {k^2 - m^2 + i\epsilon} [/tex]

but how does it disappear, and how does

[tex]k^2 - m^2 + i\epsilon [/tex] turn into

[tex]\vec{k}^2 + m^2 [/tex]

[tex] k^0 [/tex] would be the [tex]\omega [/tex]

but somehow this doesn't add up.

so just wondering if anyone could give a pointer on how to solve this

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# Confusing integral in Zee's QFT

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