Pentahedral volume, chaos, and quantum gravity

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.

8 pages, 5 figures, small revisions made and typos fixed, updated to include appendices

References in corpus (4)

• Polyhedra in loop quantum gravity
• Periodic-orbit theory of universal level correlations in quantum chaos
• Discreteness of the volume of space from Bohr-Sommerfeld quantization
• Bohr-Sommerfeld Quantization of Space

Cited by in corpus (8)

• SL(2,C) Chern-Simons Theory, a non-Planar Graph Operator, and 4D Loop Quantum Gravity with a Cosmological Constant: Semiclassical Geometry
• Matrix Elements of Lorentzian Hamiltonian Constraint in LQG
• Twisted geometries, twistors and conformal transformations
• Hamiltonian spinfoam gravity
• Chaos, Dirac observables and constraint quantization
• How many quanta are there in a quantum spacetime?
• The Large-Volume Limit of a Quantum Tetrahedron is a Quantum Harmonic Oscillator
• Classical and Quantum Polyhedra