  In SU(2) gluodynamics, the Debye gluon contribution W_D(A_0) to the effective
action of the temporal gauge field component, A_0 = const, at high temperature
is calculated in the background R^{xi} gauge. It is shown that at nonzero A_0
the standard definition k_0 = 0, |k| -> 0 corresponds to long distance
correlations for the longitudinal in internal space gluons. The transversal
gluons become screened by the A_0 background field. Therefore they give zero
contributions and have to be excluded from the correlation corrections. The
total effective action accounting for the one-loop, two-loop and correct
W_D(A_0) satisfies Nielsen's identity that proves gauge invariance of the A_0
condensation phenomenon.
