Conserved quantities in isotropic loop quantum cosmology

TL;DR

This paper introduces a conserved quantity in isotropic loop quantum cosmology models, linking semi-classical wavefunction limits and providing insights into the quantum gravitational dynamics.

Contribution

It develops an action principle for isotropic loop quantum cosmology and identifies a natural conserved quantity related to the Hamiltonian constraint.

Findings

Identifies a conserved quantity $Q$ in the difference equation.

Links semi-classical wavefunction limits at large volume.

Generalizes to difference equations from self-adjoint operators.

Abstract

We develop an action principle for those models arising from isotropic loop quantum cosmology, and show that there is a natural conserved quantity $Q$ for the discrete difference equation arising from the Hamiltonian constraint. This quantity $Q$ relates the semi-classical limit of the wavefunction at large values of the spatial volume, but opposite triad orientations. Moreover, there is a similar quantity for generic difference equations of one parameter arising from a self-adjoint operator.