A simple sum rule for the thermal gluon spectral function and applications

In this paper, we derive a simple sum rule satisfied by the gluon spectral function at finite temperature. This sum rule is useful in order to calculate exactly some integrals that appear frequently in the photon or dilepton production rate by a quark gluon plasma. Using this sum rule, we rederive simply some known results and obtain some new results that would be extremely difficult to justify otherwise. In particular, we derive an exact expression for the collision integral that appears in the calculation of the Landau-Pomeranchuk-Migdal effect.