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@masterthesis{faucris.108049744,
abstract = {The dynamical laws of an evolving system determine how the system will look at later times, given some initial state the system started from. In quantum cosmology, one ap- plies this idea to the earliest moments of the universe, which requires one to have some idea about the intial conditions at the beginning of time. One proposal describing these initial conditions in the context of canonical quantum gravity is due to Hartle and Hawk- ing. Their proposal entails a preferred initial state for the universe which is based on a Euclidean path integral over all compact positive definite four-geometries which have a given three-geometry as a boundary. The wave function constructed this way satisfies the constraint equations of general relativity in ADM variables in a formal sense.
Following the connection formulation, general relativity can be equivalently recast using the so-called Ashtekar-Barbero variables. The idea followed in this thesis is to mimic Hartle’s and Hawking’s procedure to construct an initial state in terms of these new variables. We observe that the wave function constructed this way does not satisfy the constraint equations of loop quantum gravity, even in a formal sense. We investigate this issue in the simple case of a relativistic particle. We finally suggest a modification of the proposal that does satisfy the constraints at least in a formal sense and start to consider its implications in quantum cosmology.

},
author = {Dhandhukiya, Satya and Sahlmann, Hanno},
faupublication = {yes},
peerreviewed = {automatic},
school = {Friedrich-Alexander-Universität Erlangen-Nürnberg},
title = {{On} the {Hartle}-{Hawking} state for loop quantum gravity},
year = {2016}
}
@article{faucris.109996304,
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.},
author = {Dhandhukiya, Satya and Sahlmann, Hanno},
doi = {10.1103/PhysRevD.95.084047},
faupublication = {yes},
journal = {Physical Review D},
peerreviewed = {unknown},
title = {{Towards} {Hartle}-{Hawking} states for connection variables},
volume = {95},
year = {2017}
}