Higher Order Thermal Corrections to Photon Self Energy

We investigate temperature behavior up to two loop level in QED in the background heat bath using real time formalism. The thermal correction to the coupling constant in QED at low temperature are presented up to the two loop level. It is observed that the removal of singularities at the two loop level is only possible if the integrations of loop momenta are done in a specific order. Some of the possible applications of the results are also indicated.