Landau-Pomeranchuk-Migdal effect in thermal field theory

In recent studies, the production rate of photons or lepton pairs by a quark gluon plasma has been found to be enhanced due to colinear singularities. This enhancement pattern is very dependent on rather strict collinearity conditions between the photon and the quark momenta. It was estimated assuming stable quasi-particles. In this paper, we study the modifications of this collinear enhancement when we take into account the possibility for the quarks to have a finite lifetime. Assuming a lifetime of order $(g^2T\ln(1/g))^{-1}$, we find that only low invariant mass photons are affected. The region where finite lifetime effects are important can be interpreted as the region where the Landau-Pomeranchuk-Migdal effect plays a role in thermal photon production by bremsstrahlung. It is also found that this effect modifies the spectrum of very energetic photons. Based on these results and on a previous work on infrared singularities, we end this paper by a reasonable physical picture for photon production by a quark gluon plasma, that should be useful to set directions for future technical developments.