Magnetic screening in the hot gluon system

The gluon transverse self-energy of the pure Yang–Mills system at high-temperature is analysed in the static limit and at fourth order in the coupling. Possible contributions to this function are collected, seen to be gauge-fixing independent subsets and shown to vanish all, except those which are either regulators or constituents of the self-energy of Euklidean 3D Yang–Mills theory at zero temperature. The latter self-energy, in turn, is known from the non-perturbative analysis by Karabali and Nair.