Pentahedral volume, chaos, and quantum gravity
General Relativity and Quantum Cosmology
2014-03-12 v2 Mathematical Physics
math.MP
Abstract
We show that chaotic classical dynamics associated to the volume of discrete grains of space leads to quantal spectra that are gapped between zero and nonzero volume. This strengthens the connection between spectral discreteness in the quantum geometry of gravity and tame ultraviolet behavior. We complete a detailed analysis of the geometry of a pentahedron, providing new insights into the volume operator and evidence of classical chaos in the dynamics it generates. These results reveal an unexplored realm of application for chaos in quantum gravity.
Keywords
Cite
@article{arxiv.1211.7311,
title = {Pentahedral volume, chaos, and quantum gravity},
author = {Hal M. Haggard},
journal= {arXiv preprint arXiv:1211.7311},
year = {2014}
}
Comments
8 pages, 5 figures, small revisions made and typos fixed, updated to include appendices