Vacuum Energy Density near Fluctuating Boundaries
  The imposition of boundary conditions upon a quantized field can lead to singular energy densities on the boundary. We treat the boundaries as quantum mechanical objects with a nonzero position uncertainty, and show that the singular energy density is removed. This treatment also resolves a long standing paradox concerning the total energy of the minimally coupled and conformally coupled scalar fields. 
L.H. Ford and N.F. Svaiter