Cancellation of Infrared Divergences in Thermal QED

Abstract

As a preliminary step, the radiation produced by a classical charged current coupled to a quantized $A_μ$ is solved. To each order in $α$, all infrared divergences cancel between the virtual $γ$'s and the real $γ$'s absorbed from the plasma or emitted into the plasma. When all orders of perturbation theory are summed, the finite answer predicts a suppression of radiation with $ω< αT$. The analysis of QED then consists of two steps. First, a general probability at $T\neq 0$ is organized so that all the virtual $e^{\pm},γ$ are in the amplitudes and all the real $e^{\pm},γ$ are in the phase space integrations. Next, the cancellations of IR divergences between virtual and real are demonstrated.