Two-loop vacuum polarization in QED at finite temperature
Abstract
The self-energy of photons at finite temperature is presented, up to the two-loop corrections, using the real-time formalism. The renormalized coupling constant has been derived in a form that is relevant for all the temperature ranges of interest in QED, specifically for the temperatures around T∼m, where m is the electron mass. Finite temperature modification mainly comes through the hot fermions when T≥m. We use the calculations for the vacuum polarization to determine the dynamically generated mass of the photon, Debye screening length, and plasma frequency up to order α2 as well as the electromagnetic properties of the background medium in the temperature range m≤T≤2m. At higher temperatures, the existing renormalization scheme does not work well because of the increase in the coupling constant. To exactly determine the validity of the renormalization scheme, the higher order calculations are required. The temperature, T∼m, is of specific interest from the point of view of the early universe. Such calculations have also recently acquired significance due to the possibility of producing electron–positron plasma in the laboratory.
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