Infrared divergence of quantum electrodynamics at finite temperature

It is proved that the necessary and sufficient condition for cancellation of the infrared divergence at finite temperature is that it cancel in vacuo. The specified c-number current problem provides a theoretical laboratory to study the effects of stimulation and is solved exactly at finite temperature. The methods of finite-temperature field theory are used to extract the infrared divergence of quantum electrodynamics at finite temperature to all orders in α. The potential divergence is promoted by stimulation from logarithmic to an inverse power in k). As a by-product, the Ward identities and renormalization constants of finite-temperature field theory are obtained. Approximate expressions for the radiative corrections at finite temperature are given