(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I don't understand how Zee gets Eq. (2) on p. 24:

[itex]W(J) = - \frac{1}{2}\int \frac{d^4k}{(2\pi)^4} J(k)^\ast\frac{1}{k^2-m^2+i\varepsilon}J(k)[/itex]

2. Relevant equations

[itex]W(J) := - \frac{1}{2}\int d^4x\int d^4y J(x)D(x-y)J(y)[/itex]

3. The attempt at a solution

I don't see where the [itex]d^4k[/itex] and factors of 2pi are coming from. Manipulating the definition of W(J) I was able to show that

[itex]W(J) = -\frac{1}{2}\int d^4 x e^{ikx}J(x)\frac{1}{k^2-m^2+i\varepsilon} J(k)[/itex]

[itex]W(J) = -\frac{1}{2}J(-k)\frac{1}{k^2-m^2+i\varepsilon} J(k)[/itex]

but this obviously doesn't agree.

Thanks.

**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!

# Homework Help: QFT in a nutshell: From field to particle

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