Loop Quantum Gravity and Asymptotically Flat Spaces

After motivating why the study of asymptotically flat spaces is important in loop quantum gravity, we review the extension of the standard framework of this theory to the asymptotically flat sector detailed in [1]. In particular, we provide a general procedure for constructing new Hilbert spaces for loop quantum gravity on non-compact spatial manifolds. States in these Hilbert spaces can be interpreted as describing fluctuations around fiducial fixed backgrounds. When the backgrounds are chosen to approximate classical asymptotically flat 3-geometries this gives a natural framework in which to discuss physical applications of loop quantum gravity, especially its semi-classical limit. We present three general proposals for the construction of suitable backgrounds, including one approach that can lead to quantum gravity on anti-DeSitter space as described by the Chern-Simons state. 1 Motivating Asymptotic Flatness Remarkable progress has been made in the field of non-perturbative (loop) quantum gravity in the last decade or so and it is now a rigorously defined kinematical theory. We are at the stage where physical applications of loop quantum gravity can be studied and used to provide checks for the consistency of the quantisation programme. Equally, old fundamental problems of canonical quantum gravity such as the problem of time or the interpretation of quantum cosmology need to be reevaluated seriously. The purpose of this report is to suggest that all these issues can be tackled most profitably in the asymptotically flat sector of quantum gravity and ∗[email protected]