The stress tensor of a massive scalar field, as an integral over normal modes (which are not mere plane waves), is regularized by covariant point separation. When the expectation value in a Parker-Fulling adiabatic vacuum state is expanded in the limit of small curvature-to-mass ratios, the series coincides in each order with the Schwinger-DeWitt-Christensen proper-time expansion. The renormalization ansatz suggested by these expansions (which applies to arbitrary curvature-to-mass ratios and arbitrary quantum state) can be implemented at the integrand level for practical computations. The renormalized tensor (1) passes in the massless limit, for approprite choice of state, to the known vacuum stress of a massless field, (2) agrees with the explicit results of Bernard and Duncan for a special model, (3) has a nonzero vacuum expectation value in the two-dimensional "Milne universe" (flat space in hyperbolic coordinates). Following Wald, we prove that the renormalized tensor is conserved and point out that there is no arbitrariness in the renormalization procedure. The general approach of this paper is applicable to four-dimensional models.

• Received 4 May 1978

DOI:https://doi.org/10.1103/PhysRevD.18.4435