Non-Abelian gauge couplings at finite temperature in the general covariant gauge

By the use of the real-time formalism of field theory at finite temperature we carry out the one-loop off-shell calculation for massless non-Abelian gauge theories at finite temperature in the general covariant gauge, and study the properties of the temperature- and gauge-dependent couplings, a(μ,ξ≡T/μ;α). The effects of temperature manifest themselves as a powerlike behavior of the inverse of the coupling $a^{\mathrm{-}1}$(μ,ξ;α) on the parameter ξ=T/μ, in sharp contrast to the logarithmic dependence on the momentum μ. The strong vertex dependence of the coupling is shown to come out irrespective of any choice of the gauge parameter α within the covariant gauge, and thus may invalidate the perturbative treatment of gauge theory at finite (especially at high) temperature.