  The free energy due to the vacuum fluctuations of matter fields on a
classical gravitational background is discussed. It is shown explicitly how
this energy is calculated for a non-minimally coupled scalar field in an
arbitrary gravitational background, using the heat kernel method. The treatment
of (self-)interacting fields of higher spin is outlined, using a meanfield
approximation to the gaugefield when treating the gauge boson self interaction
and the fermion-gauge boson interaction.
