Year: 2017
Type: article
Abstract: The Hartle-Hawking state is a proposal for a preferred initial state for quantum gravity, based on a path integral over all compact Euclidean four-geometries which have a given three-geometry as a boundary. The wave function constructed this way satisfies the (Lorentzian) Hamiltonian constraint of general relativity in ADM variables in a formal sense. In this article, we address the question of whether this construction is dependent on the canonical variables used. We give a precise derivation of the properties of the Hartle-Hawking state in terms of formal manipulations of the path integral expressions. Then we mimic the construction in terms of Ashtekar-Barbero variables, and observe that the resulting wave function does not satisfy the Lorentzian Hamiltonian constraint even in a formal sense. We also investigate this issue for the relativistic particle, with a similar conclusion. We finally suggest a modification of the proposal that does satisfy the constraint at least in a formal sense and start to consider its implications in quantum cosmology. We find that for certain variables, and in the saddle point approximation, the state is very similar to the Ashtekar-Lewandowski state of loop quantum gravity. In the process, we have calculated the on-shell action for several cosmological models in connection variables.
Authors: Satya Dhandhukiya, Hanno Sahlmann
Institution: Friedrich-Alexander-Universität Erlangen-Nürnberg
Language: English
Subfield: Statistical and Nonlinear Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2508815016