The Functional Schrodinger Equation in the Semiclassical Limit of Quantum Gravity with a Gaussian Clock Field
arXiv:2008.13469 · doi:10.3390/universe6100176
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.
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