Vacuum energy density in arbitrary background fields

Abstract

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