Nielsen's identity and gluon condensation at finite temperature.

Abstract

The problem of the gauge dependence of the zero gauge field component condensate, ${\mathit{A}}_{0}$=const, is investigated in finite temperature SU(3) gluodynamics. The two-loop effective action W(${\mathit{A}}_{0}$,\ensuremath{\xi}) is recalculated in the background ${\mathit{R}}_{\ensuremath{\xi}}$ gauge. The obtained result somewhat differs from that of other authors. By straightforward calculation it is shown that the two-loop effective action W(${\mathit{A}}_{0}$,\ensuremath{\xi}) satisfies the generalized Nielsen (Ward-type) identity and has a nontrivial minimum. Hence, gauge invariance of the gluon condensation phenomenon is derived. A comparison with Belyaev's method and results are also discussed.