I'm a bit embarrassed to post this, as it might be trivial but what the hey? I'm stuck!
The problem is to reduce this:
There is going to be a factor of -2i in the process.
If it matters, there is an integration over all k in the unreduced form. These (minus a couple of numerical factors) are the intregrands.
More information upon request.
Just for completeness, the Minkowski four-vector for k is . In case you need it.