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## Homework Statement

How does one actually solve the integral for the Wightman function for a massless quantum scalar field in 4D Minkowski spacetime? That is, what is the integration technique to go from:

[itex] \langle \hat{\phi}(x) \hat{\phi}(y) \rangle = \int_c d^4k \, \frac{1}{(2 \pi )^4}\frac{e^{ik(x-y)}}{ k^2} [/itex]

to:

[itex] \langle \hat{\phi}(x) \hat{\phi}(y) \rangle = \frac{1}{4 \pi^2 (x-y)^2} [/itex]?

## Homework Equations

See above.

## The Attempt at a Solution

The [itex]k_0[/itex] term is dealt with by contour integration. That part's easy. The problem I'm having is figuring out how to deal with the [itex]k_i[/itex] terms. It should just be a 3D Fourier transform, but I can't figure it out.

I have to admit that it's embarrassing for me to post this, since I'm a postdoc and should know this off the top of my head. I know I have the answer buried somewhere in my notes, but I just finished an oversees move and all of my notes are still in transit. I haven't been able to find it online, either; seems most online lecture notes I've found either just show the final equation or leave the derivation as an exercise to the student. (Ha!)

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