M. Cavaglia et V. Dealfaro, QUANTIZATION OF AN INTEGRABLE MINISUPERSPACE MODEL IN DILATON-EINSTEIN GRAVITY, International journal of modern physics D, 6(1), 1997, pp. 39-47
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 an
d identify canonical quantities that generate rigid symmetries of the
Hamiltonian. Quantization is performed both by the Dirac and the reduc
ed methods. Since the system is classically integrable we show that bo
th approaches lead to the same positive definite Hilbert space.