Photon Emission from Ultrarelativistic Plasmas

The emission rate of photons from a hot, weakly coupled ultrarelativistic plasma is analyzed. Leading-log results, reflecting the sensitivity of the emission rate to scattering events with momentum transfers from $gT$ to $T$, have previously been obtained. But a complete leading-order treatment requires including collinearly enhanced, inelastic processes such as bremsstrahlung. These inelastic processes receive O(1) modifications from multiple scattering during the photon emission process, which limits the coherence length of the emitted radiation (the Landau-Pomeranchuk-Migdal effect). We perform a diagrammatic analysis to identify, and sum, all leading-order contributions. We find that the leading-order photon emission rate is not sensitive to non-perturbative $g^2 T$ scale dynamics. We derive an integral equation for the photon emission rate which is very similar to the result of Migdal in his original discussion of the LPM effect. The accurate solution of this integral equation for specific theories of interest will be reported in a companion paper.