On a Continuum Limit for Loop Quantum Cosmology

TL;DR

This paper explores the continuum limit of Loop Quantum Cosmology by adapting a program for polymeric theories, aiming to address regulator ambiguities and connect LQC with classical theories.

Contribution

It introduces a reformulation of the continuum limit problem in LQC within a broader framework for polymeric theories, extending previous methods to cosmological models.

Findings

Initial steps toward a continuum limit formulation for LQC.

Potential resolution of regulator ambiguity in LQC.

Framework applicable to other polymeric quantum systems.

Abstract

The use of non-regular representations of the Heisenberg-Weyl commutation relations has proved to be useful for studying conceptual and technical issues in quantum gravity. Of particular relevance is the study of Loop Quantum Cosmology (LQC), a symmetry reduced theory that is related to Loop Quantum Gravity, and that is based on a non-regular, polymeric representation. Recently, a soluble model was used by Ashtekar, Corichi and Singh to study the relation between Loop Quantum Cosmology and the standard Wheeler-DeWitt theory and in particular the passage to the limit in which the auxiliary parameter (interpreted as "quantum geometry discreetness") is sent to zero in hope to get rid of this `regulator ambiguity' in the LQC dynamics. In this note we outline the first steps toward reformulating this question within the program developed by the authors for studying the continuum limit of polymeric theories, which was successfully applied to simple systems such as a Simple Harmonic Oscillator and the Free Particle.