  The thermal self-energy of gluons generally depends on four Lorentz-invariant
functions. Only two of these occur in the hard thermal loop approximation of
Braaten and Pisarski because of the abelian Ward identity
$K_{\mu}\Pi^{\mu\nu}_{\rm htl}=0$. However, for the exact self-energy
$K_{\mu}\Pi^{\mu\nu}\neq 0$. In linear gauges the Slavnov-Taylor identity is
shown to require a non-linear relation among three of the Lorentz-invariant
self-energy function: $(\Pi_{C})^{2}=(K^{2}-\Pi_{L})\Pi_{D}$. This reduces the
exact gluon propagator to a simple form containing only two types of poles: one
that determines the behavior of transverse electric and magnetic gluons and one
that controls the longitudinally polarized electric gluons.
