A Solution of the Discrete Wheeler–Dewitt Equation in the Vicinity of Small Scale Factors and Quantum Mechanics in the Space of Negative Constant Curvature

Abstract

The asymptotic of the solution of the discrete Wheeler–DeWitt equation is found in the vicinity of small scale factors. It is shown that the problem is equivalent to the solution of the stationary Schr¨odinger equation in the (super) space of negative constant curvature. The minimum positive eigenvalue is found from which a continuous spectrum begins.