QED corrections to Planck's radiation law and photon thermodynamics

Leading corrections to Planck's radiation formula and other photon thermodynamic functions arising from the pair-mediated photon-photon interaction are calculated. This interaction is found to be attractive and to cause a small increase in occupation number for all modes and a corresponding correction to the equation of state. The results are valid for the range of temperatures well below [ital T][sub [ital e]]=5.9 GK, the temperature equivalent to the electron mass, a range for which the photon gas is essentially free of pair-produced electrons and positrons. An interesting effect of these corrections is the behavior of the photon gas as an elastic medium and its ability to propagate density perturbations. It is found that the cosmic photon gas subsequent to electron-positron annihilation would have manifested these elastic properties were it not for the presence of the free electrons and their dominance of the photon thermodynamics.