On the Relation between Classical and Quantum Cosmology in a 2-Dimensional Dilaton-Gravity Model

Abstract

We analyse the classical and quantum theory of a scalar field interacting with gravitation in two dimensions. We describe a class of analytic solutions to the Wheeler-DeWitt equation from which we are able to synthesise states that give prominence to a set of classical cosmologies. These states relate in a remarkable way to the general solution of the classical field equations. We express these relations, without approximation, in terms of a metric and a closed form on the domain of quantum states.