Radiative Corrections to the Stefan-Boltzmann Law

Photons in blackbody radiation have non-zero interactions due to their couplings to virtual electron-positron pairs in the vacuum. For temperatures much less than the electron mass $m$ these effects can be described by an effective theory incorporating the Uehling and Euler-Heisenberg interactions as dominant terms. By a redefinition of the electromagnetic field, the Uehling term is shown not to contribute. The Stefan-Boltzmann energy is then modified by a term proportional with $T^8\mathrm{/}{m}^4$ in agreement with the semi-classical result of Barton. The same effects give a speed of light smaller than one at non-zero temperatures as has also recently been derived using full QED.