Quantum Cosmological Approach to 2d Dilaton Gravity

TL;DR

This paper explores the canonical quantization of 2d dilaton gravity models, solving Wheeler-DeWitt equations, establishing quantum equivalence, and relating quantum states to classical solutions.

Contribution

It provides a detailed quantum analysis of the induced 2d-gravity and CGHS models, including solutions and the ground state wavefunction, advancing understanding of quantum 2d gravity.

Findings

Solutions to Wheeler-DeWitt equations in homogeneous models

Quantum equivalence between induced 2d-gravity and CGHS models

Proposal of a ground state wavefunction

Abstract

We study the canonical quantization of the induced 2d-gravity and the pure gravity CGHS-model on a closed spatial section. The Wheeler-DeWitt equations are solved in (spatially homogeneous) choices of the internal time variable and the space of solutions is properly truncated to provide the physical Hilbert space. We establish the quantum equivalence of both models and relate the results with the covariant phase-space quantization. We also discuss the relation between the quantum wavefunctions and the classical space-time solutions and propose the wave function representing the ground state.