Quantum Observables and Recollapsing Dynamics

TL;DR

This paper develops a quantization scheme for time reparametrization invariant systems, constructing observables that align with classical physics predictions of recollapse in certain cosmological models.

Contribution

It introduces a method to construct a complete set of observables for finite-dimensional invariant systems, linking quantum results with classical recollapse predictions.

Findings

Constructed densely defined operators on the physical Hilbert space.

Operators have clear classical interpretations.

Quantization predicts recollapse in specific cosmological models.

Abstract

Within a simple quantization scheme, observables for a large class of finite dimensional time reparametrization invariant systems may be constructed by integration over the manifold of time labels. This procedure is shown to produce a complete set of densely defined operators on a physical Hilbert space for which an inner product is identified and to provide reasonable results for simple test cases. Furthermore, many of these observables have a clear interpretation in the classical limit and we use this to demonstrate that, for a class of minisuperspace models including LRS Bianchi IX and the Kantowski-Sachs model this quantization agrees with classical physics in predicting that such spacetimes recollapse.