Longitudinal polarization in Feynman photon propagator?

[copernicus1]

For internal photon states, is it necessary to sum over the longitudinal polarization state in addition to the transverse states? And if so, does the ordinary Feynman-gauge propagator take care of this?

Thanks!

 

[Avodyne]

No. However, the longitudinal states do not couple to the conserved electromagnetic current, so it doesn't matter whether you include them or not. Thus the $k^\mu k^\nu$ term in the propagator can be multiplied by an arbitrary number (this is sometimes called "generalized Feynman gauge"), and the scattering amplitudes do not depend on that number.