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 this problem is equivalent to the solution of the stationary Schr\"{o}dinger equation in the (super) space of negative constant curvature. The minimum positive eigenvalue is found from which a continuous spectrum begins.