Landau–Pomeranchuk–Migdal effect in a quark–gluon plasma and the Boltzmann equation

We show how the Landau–Pomeranchuk–Migdal effect on photon production rates in a quark–gluon plasma can be derived via the usual Boltzmann equation. To do this, we first derive the electromagnetic polarization tensor using linear response theory, and then formulate the Boltzmann equation including the collisions mediated by soft gluon exchanges. We then identify the resulting expression for the production rate with that obtained by the field-theoretic formalism recently proposed by Arnold, Moore and Yaffe. To illustrate the LPM effect we solve the Boltzmann equation in the diffusion approximation.