Born-Oppenheimer meets Wigner-Weyl in Quantum Gravity
A. Y. Kamenshchik, A. Tronconi, G. Venturi
TL;DR
This paper combines Born-Oppenheimer and Wigner-Weyl methods to analyze the quantum-to-classical transition in quantum cosmology, deriving equations for the scale factor and matter evolution, including higher order corrections.
Contribution
It introduces a novel approach by applying Wigner-Weyl transformation to the Born-Oppenheimer-decomposed Wheeler-DeWitt equation in quantum cosmology.
Findings
Reproduces the Friedmann equation in the classical limit
Derives equations for matter evolution
Provides expressions for higher order semi-classical corrections
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.
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