Spectral properties of the quantum Mixmaster universe
General Relativity and Quantum Cosmology
2017-09-06 v3 Mathematical Physics
math.MP
Quantum Physics
Abstract
We study the spectral properties of the anisotropic part of Hamiltonian entering the quantum dynamics of the Mixmaster universe. We derive the explicit asymptotic expressions for the energy spectrum in the limit of large and small volumes of the universe. Then we study the threshold condition between both regimes. Finally we prove that the spectrum is purely discrete for any volume of the universe. Our results validate and improve the known approximations to the anisotropy potential. They should be useful for any approach to the quantization of the Mixmaster universe.
Keywords
Cite
@article{arxiv.1703.08462,
title = {Spectral properties of the quantum Mixmaster universe},
author = {Hervé Bergeron and Ewa Czuchry and Jean-Pierre Gazeau and Przemysław Małkiewicz},
journal= {arXiv preprint arXiv:1703.08462},
year = {2017}
}
Comments
Version accepted by Phys. Rev. D