Fourier tr. of dirac delta in minkowski space

[fliptomato]

Hey everyone, a quick question: what is the Fourier space representation of the dirac delta function in minkowski space? It should be some integral over e^{ikx} (with some normalization with 2*pi's). I'm curious if the "kx" is a dot product in the minkowski or euclidean sense, and how one reasons this.

Any thoughts? =)
Flip

 

[dextercioby]

Well, of course

\delta^{4}\left(x-x'\right) =\frac{1}{\left(2\pi\right)^4}\int_{M_{4}} d^{4}k \ e^{ik^{\mu}\left(x-x'\right)_{\mu}

where the metric on M_{4} is (conventionally) diag(+,-,-,-).

Daniel.