Minisuperspace models of discrete systems

TL;DR

This paper introduces discrete quantum spin systems as models for canonical quantum gravity, analyzing their dynamics, correlations, and stability through various methods, including minisuperspace models and continuum limits.

Contribution

It develops and evaluates different homogeneous minisuperspace models for discrete quantum systems, demonstrating their effectiveness and the importance of non-perturbative analysis for long-range correlations.

Findings

Effective methods agree with operator calculations.

Long-range correlations require non-perturbative solutions.

Matter couplings may influence stability analysis.

Abstract

A discrete quantum spin system is presented in which several modern methods of canonical quantum gravity can be tested with promising results. In particular, features of interacting dynamics are analyzed with an emphasis on homogeneous configurations and the dynamical building-up and stability of long-range correlations. Different types of homogeneous minisuperspace models are introduced for the system, including one based on condensate states, and shown to capture different aspects of the discrete system. They are evaluated with effective methods and by means of continuum limits, showing good agreement with operator calculations whenever the latter are available. As a possibly quite general result, it is concluded that an analysis of the building-up of long-range correlations in discrete systems requires non-perturbative solutions of the dynamical equations. Some questions related to stability can be analyzed perturbatively, but suggest that matter couplings may be relevant for this question in the context of quantum cosmology.