Mode decomposition and renormalization in semiclassical gravity - art. no.107503

We compute the influence action for a system perturbatively coupled to a li near scalar field acting as the environment. Subtleties related to divergen ces that appear when summing over all the modes are made explicit and clari fied. Being closely connected with models used in the literature, we show h ow to completely reconcile the results obtained in the context of stochasti c semiclassical gravity when using mode decomposition with those obtained b y other standard functional techniques. [S0556-2821(99)08020-0].