Static quantization of two-dimensional dilaton gravity and black holes (Q1576055)

For two-dimensional dilaton gravity (without matter) which may be classically reduced to a gauge \((0+1)\)-dimensional theory, the authors propose a static quantization scheme which yields a simple gauge-invariant quantum mechanics. The various properties of the gauge-invariant operators and the Hilbert space of states are determined. The principal result is that for \(N\)-dimensional pure gravity with \((N-2)\)-dimensional spherical symmetry, the square of the Arnowitt-Deser-Misner mass operator is selfadjoint. Contents includes: introduction, general canonical theory, spherically symmetric gravity, quantization, conclusions.