Integral Hilbert spaces and the dynamics of loop quantum cosmos
Abstract
Polymer quantization program applied in Loop Quantum Gravity/Cosmology leads to nonseparable Hilbert spaces. Commonly, one sidesteps this problem by singling out and working with a separable superselection sector. This is however often no longer accessible in more involved models beyond isotropic ones. In an alternative approach one builds a separable Hilbert space as an integral over all available sectors. Here we test the dynamics following from the latter on the example of a flat isotropic Universe admitting negative cosmological constant and a massless scalar field. There, numerical evolution of (initially) semiclassical states shows that there is no relevant difference in their long term semiclassicality properties in comparison to those in a single sector approach. Further, the older (problem-specific) numerical methods are compared against an application of more common and more efficient standard tools (eigen library).
Versions
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BibTeX
@misc{kozicki2026integral,
title = {{Integral Hilbert spaces and the dynamics of loop quantum cosmos}},
author = {Janek Kozicki and Tomasz Pawłowski},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2608.02798},
eprint = {2608.02798},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2608.02798},
}
RIS
TY - UNPB
TI - Integral Hilbert spaces and the dynamics of loop quantum cosmos
AU - Janek Kozicki
AU - Tomasz Pawłowski
PY - 2026
DA - 2026/09/28
PB - arXiv
DO - 10.48550/arxiv.2608.02798
UR - https://arxiv.org/abs/2608.02798
AB - Polymer quantization program applied in Loop Quantum Gravity/Cosmology leads to nonseparable Hilbert spaces. Commonly, one sidesteps this problem by singling out and working with a separable superselection sector. This is however often no longer accessible in more involved models beyond isotropic ones. In an alternative approach one builds a separable Hilbert space as an integral over all available sectors. Here we test the dynamics following from the latter on the example of a flat isotropic Universe admitting negative cosmological constant and a massless scalar field. There, numerical evolution of (initially) semiclassical states shows that there is no relevant difference in their long term semiclassicality properties in comparison to those in a single sector approach. Further, the older (problem-specific) numerical methods are compared against an application of more common and more efficient standard tools (eigen library).
ER -