Quantization of a 2D Minisuperspace Model in Dilaton-Einstein Gravity

TL;DR

This paper explores the quantization of a 2D minisuperspace model in dilaton-Einstein gravity, revealing consistent quantum descriptions for static and Kantowski-Sachs-like universes.

Contribution

It develops canonical formalisms and applies Dirac and reduced quantization methods to a dilaton-Einstein minisuperspace model, demonstrating their equivalence.

Findings

Both quantization methods yield the same positive definite Hilbert space.

Canonical quantities generating symmetries are identified.

The model describes static and Kantowski-Sachs-like universes.

Abstract

We investigate a minisuperspace model of Einstein gravity plus dilaton that describes a static spherically symmetric configuration or a Kantowski - Sachs like universe. We develop the canonical formalism and identify canonical quantities that generate rigid symmetries of the Hamiltonian. Quantization is performed by the Dirac and the reduced methods. Both approaches lead to the same positive definite Hilbert space.