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:

$\displaystyle e^{i \bold{k} \cdot ( \bold{x} - \bold{y} ) } e^{-i k_0 (x_0 - y_0) } - e^{-i \bold{k} \cdot ( \bold{x} - \bold{y} ) } e^{i k_0 (x_0 - y_ 0 ) }$

into this:

$\displaystyle e^{ i \bold{k} \cdot ( \bold{x} - \bold{y} ) } ~ sin( k_0 (x_0 - y_0 ))$

There is going to be a factor of -2i in the process.

If it matters, there is an integration over allkin the unreduced form. These (minus a couple of numerical factors) are the intregrands.

More information upon request.

-Dan

Just for completeness, the Minkowski four-vector for k is $\displaystyle k^{\mu} = ( -k_0, \bold{k} )$. In case you need it.