Mode decomposition and renormalization in semiclassical gravity

TL;DR

This paper clarifies the divergences and mode decomposition issues in semiclassical gravity, reconciling different computational approaches to influence actions in stochastic semiclassical gravity.

Contribution

It provides a detailed analysis of divergences in mode sums and demonstrates how to reconcile mode decomposition results with standard functional methods in semiclassical gravity.

Findings

Clarified divergences in mode summation

Reconciled mode decomposition with functional techniques

Enhanced understanding of influence action in semiclassical gravity

Abstract

We compute the influence action for a system perturbatively coupled to a linear scalar field acting as the environment. Subtleties related to divergences that appear when summing over all the modes are made explicit and clarified. Being closely connected with models used in the literature, we show how to completely reconcile the results obtained in the context of stochastic semiclassical gravity when using mode decomposition with those obtained by other standard functional techniques.