Theory Group Final Defense, 15 August 2017
Justin Feng, UT Theory Group
Temporal Insights from the End of Space
In this talk, I will present a (nonrigorous) derivation of the Wheeler-DeWitt equation from the path intregral for quantum General Relativity by way of boundary (Weiss) variations. One feature of this approach is that it does not require an exact 3+1 splitting of spacetime in the bulk. For spacetimes with spatial boundary, I show that the dependence of the transition amplitudes on spatial boundary conditions is determined by a Wheeler-DeWitt equation for the spatial boundary surface. Variations in the induced metric at the spatial boundary can then be used to describe time evolution; time evolution in quantum General Relativity is therefore governed by boundary conditions on the gravitational field at the spatial boundary.