Influence functional in two dimensional dilaton gravity

TL;DR

This paper computes the influence functional in two-dimensional dilaton gravity models, analyzing quantum effects, conformal invariance, and the transition to classicality, with implications for semiclassical approximations.

Contribution

It provides an exact computation of the influence functional in conformal two-dimensional dilaton gravity and explores how dilaton loops affect semiclassical validity.

Findings

Exact influence functional in conformal case derived

Semiclassical approximation invalid without dilaton loops

Dilaton loops restore semiclassical validity

Abstract

We evaluate the influence functional for two dimensional models of dilaton gravity. This functional is exactly computed when the conformal invariance is preserved, and it can be written as the difference between the Liouville actions on each closed-time-path branch plus a boundary term. From the influence action we derive the covariant form of the semiclassical field equations. We also study the quantum to classical transition in cosmological backgrounds. In the conformal case we show that the semiclassical approximation is not valid because there is no imaginary part in the influence action. Finally we show that the inclusion of the dilaton loop in the influence functional breaks conformal invariance and ensures the validity of the semiclassical approximation.