Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
1992-11-30
Int. J. Mod. Phys. A8 (1993) 4897-4914
Physics
High Energy Physics
High Energy Physics - Theory
phyztex, UT-Komaba 92-14. A few misleading sentences are corrected and some references are added
Scientific paper
10.1142/S0217751X93001922
We study the quantum theory of 1+1 dimensional dilaton gravity, which is an interesting toy model of the black hole dynamics. The functional measures are explicitly evaluated and the physical state conditions corresponding to the Hamiltonian and the momentum constraints are derived. It is pointed out that the constraints form the Virasoro algebra without central charge. In ADM formalism the measures are very ambiguous, but in our formalism they are explicitly defined. Then the new features which are not seen in ADM formalism come out. A singularity appears at $\df^2 =\kappa (>0) $, where $\kappa =(N-51/2)/12 $ and $ N$ is the number of matter fields. Behind the singularity the quantum mechanical region $\kappa > \df^2 >0 $ extends, where the sign of the kinetic term in the Hamiltonian constraint changes. If $\kappa <0 $, the singularity disappears. We discuss the quantum dynamics of black hole and then give a suggestion for the resolution of the information loss paradox. We also argue the quantization of the spherically symmetric gravitational system in 3+1 dimensions. In appendix the differences between the other quantum dilaton gravities and ours are clarified and our status is stressed.
Hamada Kaname
Tsuchiya Asato
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