Your first problem is easily solved:
First note that the gauge field tensor is antisymmetric, i.e. F_{\gamma\mu}=-F_{\mu\gamma}.
If \partial^\gamma F_{\gamma\mu} + m^2 A_\mu =0, then \partial^\gamma F_{\gamma\mu} = -m^2 A_\mu.
Filling this in the second equation, we have \partial^\gamma...
Does anybody know a good reference for the gluon propagator at two loop?
I need it in Feynman gauge, but to have it in light-cone gauge as well is a plus.
Preferably a paper, or a book that is common (i.e. easy to find in our university's library :-) ).
Thanks!
It is possible to introduce the gauge field in a QFT purely on geometric arguments. For simplicity, consider QED, only starting with fermions, and seeing how the gauge field naturally emerges. The observation is that the derivative of the Dirac field doesn't have a well-defined transformation...