Unknown low-energy extension of the Faddeev–Popov gauge-fixing prescription

Develop a consistent extension of the Faddeev–Popov gauge-fixing prescription for Landau gauge in Yang–Mills theory that is valid at low energies (beyond the ultraviolet regime), so that functional integrals and correlation functions are well-defined in the infrared and can be used to compute thermal averages, including the one-gluon-field average.

Background

After introducing the Landau-gauge Faddeev–Popov action to define thermal gluon averages, the text emphasizes two major difficulties. The second difficulty is fundamental: due to Gribov’s discovery of multiple gauge copies satisfying the same gauge condition, the standard Faddeev–Popov framework is only justified in the ultraviolet. Any application at lower energies requires an extension that has not yet been established.

This unknown extension is critical for nonperturbative continuum calculations of Yang–Mills correlation functions and thermodynamics. The lectures later adopt the Curci–Ferrari model as a phenomenological proxy, but they explicitly note that a first-principles extension of the Faddeev–Popov prescription at low energies remains to be developed.