Radiative corrections to hot quantum electrodynamics plasma

The problem of the radiative corrections to the thermodynamic potential in statistical quantum electrodynamics in the limit of temperatures of the order of the electron rest mass is revisited. It is argued that only longitudinal modes can contribute to the so-called correlation term of the thermodynamic potential, in agreement with the pioneering calculations made by Akhiezer-Peletminskii (Sov. Phys. JETP 11 (1960) 1316), and disagreement with the more recent calculations made by Leermakers/van der Weert (Phys. Lett. 135 (1984) 118). Analogy with the Bose-Einstein condensate and consequences for the effective potential which arises in the discussion of the phase transitions which occur in the standard model are discussed.