The Casimir Effect of Curved Space-time (formal developments)
  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. 
Karsten Bormann, Frank Antonsen