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

TL;DR

This paper explores the connection between classical and quantum cosmology within a 2D dilaton-gravity model, providing exact solutions to the Wheeler-DeWitt equation and linking quantum states to classical cosmological solutions.

Contribution

It introduces a class of analytic solutions to the Wheeler-DeWitt equation that directly relate quantum states to classical cosmologies in a 2D dilaton-gravity framework.

Findings

Derived exact solutions to the Wheeler-DeWitt equation.

Established a direct relation between quantum states and classical cosmologies.

Expressed relations in closed form without approximation.

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.