# QCD gluon propagator in axial gauge, polarization sum

1. ### tobias_

2
Hi!

I have a process with multiple feynman diagrams where gluon propagators occur. When I use an axial gauge for the gluon propagator, do I have to use the same n-vector for every propagator? Following this I wonder whether I can use the same n-vector for every polarization sum in axial gauge or have to take different ones.

Thanks, Tobias

gauge field propagator in general axial gauge:
$$G_{\mu\nu}^{ab}(q,\alpha)=\frac{-i\delta^{ab}}{q^{2}}\left(-g^{\mu\nu}-\frac{q_{\mu}n_{\nu}+q_{\nu}n_{\mu}}{qn}+q_{\mu}q_{\nu}\frac{n^{2}+\alpha q^{2}}{(qn)^{2}}\right)$$

2. ### fzero

3,005
It seems pretty clear that in deriving the propagator above, one assumes that the vector $$n_\mu$$ doesn't vary with position. If it did, you would have to compute it's Fourier transform and the momentum space Feynman rules would be more complicated. Similarly, $$n_\mu$$ is independent of gauge indices, so there's no freedom to choose different values within a given computation.

3. ### ParticleGrl

669
You can use a different gauge for each external gluon (though you have to be consistent between diagrams).

You can use a different gauge for the internal gluons (different from the external legs), but each internal gluon must be in the same gauge. Changing the vector n is a form of gauge transformation.

Last edited: Apr 1, 2011
4. ### Apotheosys

3
I'm fully aware that this post is over one year old, but could someone provide a source for the above statement or at least scetch if and why this is true?