Renormalization and radiative corrections at finite temperature

We discuss the renormalization prescription for fermions at finite temperature and describe the procedure for calculating radiative corrections. Novel features arise, such as a lack of explicit Lorentz invariance, $\frac{1}{k^2}$ singularities, and the absorption of soft photons from the background heat bath. The methods are illustrated by explicit calculation of the electron renormalization and the radiative corrections to $H\to e^{+}{e}^{-}$ (with $H$ being spin zero) in finite-temperature QED.