Born-Oppenheimer meets Wigner-Weyl in Quantum Gravity
General Relativity and Quantum Cosmology
2021-09-22 v1 Cosmology and Nongalactic Astrophysics
High Energy Physics - Theory
Abstract
Starting from a Born-Oppenheimer decomposition of the Wheeler-DeWitt equation for the quantum cosmology of the matter-gravity system, we have performed a Wigner-Weyl transformation and obtained equations involving a Wigner function for the scale factor and its conjugate momentum. This has allowed us to study in more detail than previously the approach to the classical limit of gravitation and the way time emerges in such a limit. To lowest order we reproduce the Friedmann equation and the previously obtained equation for the evolution of matter. We also obtain expressions for higher order corrections to the semi-classical limit.
Keywords
Cite
@article{arxiv.2104.07480,
title = {Born-Oppenheimer meets Wigner-Weyl in Quantum Gravity},
author = {A. Y. Kamenshchik and A. Tronconi and G. Venturi},
journal= {arXiv preprint arXiv:2104.07480},
year = {2021}
}
Comments
15 pages, no figures