Quantization of an integrable minisuperspace model in dilaton-Einstein gravity

We quantize the minisuperspace model of Einstein gravity plus dilaton that describes either 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 both by the Dirac and the reduced methods. Since the system is classically integrable we show that both approaches lead to the same positive definite Hilbert space.