QCD gluon propagator in axial gauge, polarization sum

In summary, the conversation discusses the use of an axial gauge for gluon propagators, specifically whether the same n-vector must be used for every propagator and polarization sum. It is mentioned that the vector n_\mu cannot vary with position and is independent of gauge indices, so there is no freedom to choose different values within a computation. It is also stated that while a different gauge can be used for each external gluon, the internal gluons must all be in the same gauge. This is mentioned as a form of gauge transformation. A source or explanation for this statement is requested.
  • #1
tobias_
2
0
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:
[tex]
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)
[/tex]
 
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  • #2
It seems pretty clear that in deriving the propagator above, one assumes that the vector [tex]n_\mu[/tex] 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, [tex]n_\mu[/tex] is independent of gauge indices, so there's no freedom to choose different values within a given computation.
 
  • #3
tobias_ said:
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.

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:
  • #4
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?
 

1. What is the QCD gluon propagator?

The QCD gluon propagator is a mathematical quantity that represents the probability amplitude for a gluon, the fundamental force carrier of the strong nuclear force, to propagate from one point to another in quantum chromodynamics (QCD).

2. What is axial gauge in QCD?

The axial gauge is a specific choice of gauge in QCD, which is a mathematical framework used to describe the strong nuclear force. In this gauge, the direction of the gluon's polarization is restricted to be parallel or perpendicular to a chosen reference direction, rather than being allowed to point in any direction.

3. What is the polarization sum in QCD?

The polarization sum is a mathematical technique used to calculate the probability of a virtual particle, such as a gluon, to exist at a particular energy and momentum. In QCD, this sum is used to calculate the QCD gluon propagator in axial gauge.

4. Why is the QCD gluon propagator in axial gauge important?

The QCD gluon propagator in axial gauge is important because it allows us to better understand the behavior of the strong nuclear force, which plays a crucial role in the structure of matter and the interactions between particles. It also helps us to make predictions and test our understanding of QCD.

5. How is the QCD gluon propagator in axial gauge calculated?

The QCD gluon propagator in axial gauge is calculated using mathematical equations and techniques from quantum field theory. This involves integrating over all possible energies and momenta of the gluon, taking into account the restrictions imposed by the axial gauge, to determine the probability amplitude for the gluon to propagate from one point to another.

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