ZETA-FUNCTION REGULARIZATION AND ONE-LOOP RENORMALIZATION OF FIELD FLUCTUATIONS IN CURVED SPACE-TIME

The naive zeta-function approach to regularize and renormalize the flu ctuations of a quantum field in a curved background by taking the valu e of zeta(1) is improved. The proposed method produces finite quantiti es without the need of further subtractions and finite scale-parameter ized counterterms at most also in the presence of a pole at the value s = 1 of zeta(s). This method is employed to obtain a general expressi on for the trace of the stress tensor of a non-conformal invariant sca lar field and checked on some examples. In particular, the fluctuation s of a quantum scalar field are computed in the closed Einstein univer se and similar ultrastatic manifolds for a massive field with a genera lly non-conformal coupling with the curvature. (C) 1998 Elsevier Scien ce B.V. All rights reserved.