INFLUENCE FUNCTIONAL IN 2-DIMENSIONAL DILATON GRAVITY - ART. NO. 024009

We evaluate the influence functional for two-dimensional models of dil aton gravity. This functional is exactly computed when conformal invar iance is preserved, and it can be written as the difference between th e Liouville actions on each closed-time-path branch plus a boundary te rm From the influence action we derive the covariant form of the semic lassical field equations. We also study the quantum to classical trans ition in cosmological backgrounds. In the conformal case we show that the semiclassical approximation is not valid because there is no imagi nary part in the influence action. Finally we show that the inclusion of the dilaton loop in the influence functional breaks conformal invar iance and ensures the validity of the semiclassical approximation. [S0 556-2821(98)02514-4].