Structure of the Gluon Propagator at Finite Temperature

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.