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.

• Received 24 April 1998

DOI:https://doi.org/10.1103/PhysRevD.58.065007