Quantum evolution of the Universe from $\tau=0$

TL;DR

This paper demonstrates that despite the DeWitt constraint H=0, quantum operators and their mean values can evolve over time, with singular observables in classical theory remaining singular in quantum form.

Contribution

It shows that the quantum evolution of the Universe is consistent with the H=0 constraint, challenging classical notions of singularity.

Findings

Heisenberg operators evolve with time under H=0

Mean values of observables can be time-dependent

Singular classical observables remain singular quantum mechanically

Abstract

We have shown that DeWitt constraint H=0 on the physical states of the Universe does not prevent Heisenberg operators and its mean values to evolve with time. Mean value from observable, which is singular in classical theory, is also singular in a quantum case.