Pentahedral volume, chaos, and quantum gravity

H. M. Haggard

Physical Review D 87 (044020), 2013.

We show that chaotic classical dynamics associated with 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 for the application of chaos in quantum gravity.

DOI: 10.1103/PhysRevD.87.044020

Full text: HaPentahedralVolumeChaosQG.pdf