  At energies much less than the electron mass $m$ the effects of quantum
fluctuations in the vacuum due to virtual electron loops can be included by
extending the Maxwell Lagrangian by additional non-renormalizable terms
corresponding to the Uehling and Euler-Heisenberg interactions. This effective
field theory is used to calculate the properties of the QED vacuum at
temperatures $T << m$. By a redefinition of the electromagnetic field, the
Uehling term is shown not to contribute. The Stefan-Boltzmann energy density is
thus found to be modified by a term proportional with $T^8/m^4$ in agreement
with the semi-classical result of Barton. The speed of light in blackbody
radiation is smaller than one. Similarly, the correction to the energy density
of the vacuum between two metallic parallel plates diverges like $1/m^4z^8$ at
a distance from one of the plates $z \to 0$. While the integral of the
regularized energy density is thus divergent, the regularized integral is
finite and corresponds to a correction to the Casimir force which varies with
the separation $L$ between the plates as $1/m^4L^8$. This result is in
seemingly disagreement with a previous result for the radiative correction to
the Casimir force which gives a correction varying like $1/mL^5$ in a
calculation using full QED.
