# Uniqueness of minimal loop quantum cosmology dynamics

## TL;DR

This paper demonstrates that the standard Hamiltonian in isotropic loop quantum cosmology is uniquely determined by physical criteria and minimality, with considerations of covariance and conformal transformations ensuring consistency and independence from ambiguities.

## Contribution

It establishes the uniqueness of the standard Hamiltonian in loop quantum cosmology based on physical and minimality criteria, and discusses implementing conformal transformations in quantum theory.

## Key findings

- Hamiltonian is uniquely selected by physical criteria and minimality.
- Energy density remains bounded even when minimality is relaxed.
- Infrared regulator removal ensures independence from ordering ambiguities.

## Abstract

We show that the standard Hamiltonian of isotropic loop quantum cosmology is selected by physical criteria plus one choice: that it have a `minimal' number of terms. We also show the freedom, and boundedness of energy density, even when this choice is relaxed. A criterion used is covariance under dilations, the continuous diffeomorphisms remaining in this context, which are not canonical but conformally canonical transformations. We propose how to implement conformally canonical transformations in quantum theory. Removal of the infrared regulator yields independence of ordering ambiguities.