Ghosts in Practical Calculations - Questions Answered

[earth2]

Hey guys,

I have a question about how to incorporate ghosts in practical calculations. So, from what I understand I have to add a factor of -1 for each closed gluon loop, right? But there are two ghost fields, c and \bar{c} appearing when I quantize the path integral. Does that mean that I also have in principle TWO ghost diagrams for each closed, say, gluon loop?

An example: Let's look at the two-point, 1-loop scattering in pure Yang-Mills. I will only have gluon content, so my guess for the diagrams would be:

physical1-loop = "1-loop all gluon"-"1-loop c-ghost"-"1-loop-\bar{c}-ghost".

Is that correct? I can find a clear explanation...

Thanks!

 

[fzero]

There's only one diagram with ghosts running in the loop. The ghost propagator takes a $$c$$ ghost to a $$\bar{c}$$, while the vertex is gluon-$$c$$-$$\bar{c}$$. You can never have a $$c$$ or $$\bar{c}$$ running in a loop independently.