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In this paper, we derive a simple sum rule satisfied by the gluon spectralfunction at finite temperature. This sum rule is useful in order to calculateexactly some integrals that appear frequently in the photon or dileptonproduction rate by a quark gluon plasma. Using this sum rule, we rederivesimply some known results and obtain some new results that would be extremelydifficult to justify otherwise. In particular, we derive an exact expressionfor the collision integral that appears in the calculation of theLandau-Pomeranchuk-Migdal effect.Comment: 24 latex pages, 2 postscript figure

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