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

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Confusing integral in Zee's QFT

**Physics Forums | Science Articles, Homework Help, Discussion**