Bloch-Nordsieck cancellation of infrared divergences at finite temperature

Virtual-photon corrections to the scattering of a heavy charged fermion, $M\gg T$, in a plasma result in infrared divergences that are worse than at $T=0\mathrm{}$. These divergences cancel in the observable cross section, which must include a summation over the absorption and emission of real photons that are too soft to escape the plasma. The calculation requires determining the exclusive amplitudes for photon absorption and emission at $T\ne 0$. In the semiclassical approximation of Bloch and Nordsieck the problem can be solved exactly and the finite residual effects retained.