How do we deal with Gribov ambiguities when actually calculating in quantum gauge theories? Any literature references?
The problem of Gribov ambiguities is still unsolved.
Although much is known on the topology of the Gribov copies, the full implications on the theory predictions are not known.
However, progress has been achieved in restricting the configuration space to the interior of the Gribov's horizon, which is not free from Gribov copies (thus does not solve the problem completely).
This restriction results a no-pole condition for the gluon propagator hinting that the Gribov problem is important to the infra-red behavior.
A local action for yang-Mills theories inside the first Gribov horison was obtained by Zwanziger. This action was used mainly in Lattice simulations.