Structure of the Gluon Propagator at Finite Temperature

Abstract

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 $K_{\mu }{\Pi }_{\mathrm{htl}}^{\mu \nu }=0$. However, for the exact self-energy $K_{\mu }{\Pi }^{\mu \nu }\ne 0$. 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.

21 pages, latex, no figures

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