VACUUM ENERGY DENSITY IN ARBITRARY BACKGROUND FIELDS

The vacuum expectation value of the energy-momentum tensor of a real s calar field in the presence of an arbitrary scalar background field is considered. The problem of renormalization is treated in detail. In t he special case of a background field depending on one coordinate only , we give an explicit integral representation for the renormalized vac uum energy. Three explicit examples illustrate the use of this represe ntation as well as some properties of the vacuum energy density. We fi nd that a twice continuously differentiable background potential leads to a continuous energy density.