The Functional Schrodinger Equation in the Semiclassical Limit of Quantum Gravity with a Gaussian Clock Field
General Relativity and Quantum Cosmology
2020-10-20 v4
Abstract
We derive the functional Schrodinger equation for quantum fields in curved spacetime in the semiclassical limit of quantum geometrodynamics with a Gaussian incoherent dust acting as a clock field. We perform the semiclassical limit using a WKB-type expansion of the wave functional in powers of the squared Planck mass. The functional Schrodinger equation that we obtain exhibits a functional time derivative that completes the usual definition of WKB time for curved spacetime, and the usual Schrodinger-type evolution is recovered in Minkowski spacetime.
Keywords
Cite
@article{arxiv.2008.13469,
title = {The Functional Schrodinger Equation in the Semiclassical Limit of Quantum Gravity with a Gaussian Clock Field},
author = {Marcello Rotondo},
journal= {arXiv preprint arXiv:2008.13469},
year = {2020}
}